Transmission grating and laser device using the same, and method of producing transmission grating

ABSTRACT

A transmission grating includes: first light-transmissive regions having a refractive index of n 1 ; and second light-transmissive regions having a refractive index of n 2  that is smaller than n 1 . Light-reflecting interfaces on which light transmitted through the first light-transmissive regions is incident are in parallel with one another and are inclined such that a line normal to each of light-reflecting interfaces is at an inclination angle θ with respect to the flat light-incident surface and to the flat light-emitting surface, wherein 0°&lt;θ&lt;90°. When a thickness of the first light-transmissive regions in a direction perpendicular to the light-reflecting surfaces is t 1  and a thickness of the second light-transmissive regions in a direction perpendicular to the light-reflecting surfaces is t 2 , the thickness t 2 , in μm, is in a range of 0.1/π(n 1   2 −n 2   2 ) 1/2  to t 1 .

CROSS-REFERENCE TO RELATED PATENT APPLICATION

The present application claims priority under 35 U. S. C. § 119 toJapanese Patent Application No. 2017-086432 filed on Apr. 25, 2017, thecontents of which are hereby incorporated by reference in theirentirety.

BACKGROUND

The present disclosure relates to a transmission grating and a laserdevice using the same, and a method of producing the transmissiongrating.

A wavelength beam combining (WBC) technique to increase the brightnessof semiconductor laser device is known. In this technique, laser light(beams) emitted from a plurality of semiconductor laser elements arecollimated by an optical element (collimate lens) into substantiallyparallel light and made incident on a wavelength dispersive element(reflection grating) such that the beams are overlapped bywavelength-dispersive properties of the diffraction grating (forexample, described in “Laser Beam Combining for High-Power High-RadianceSources” T. Y Fan, IEEE Journal of Selected Topics in QuantumElectronics, Vol. 11, No. 3, May/June 2005, pp. 567-577).

SUMMARY

A transmission grating experiences reflection loss at a surface absentof a grating pattern when diffracted light is transmitted therethrough.However, the above described reflection grating experiencessubstantially none of the reflection loss that occurs in a transmissiongrating, and therefore is said to provide higher diffraction efficiencycompared to that of the transmission grating.

In a WBC laser light source device, if a reflection grating is employedas the wavelength dispersive element, a first optical element, which isprovided to transmit an incident beam that is emitted from a lightsource and incident on the wavelength dispersive element, and a secondoptical element, which is provided to transmit an emission beam from thewavelength dispersive element, are needed to be located at the same sidewhen seen from the wavelength dispersive element side. Increasing thenumber of laser elements in the laser light source device to achievehigher optical output would require an increase in the size of the firstoptical element to transmit the incident beams to the wavelengthdispersive element. When the size of the first optical element isincreased, the space required for the first optical element and thespace required for the second optical element would be difficult to beseparated from each other in such a WBC laser light source device. Thisimposes a limitation on the number of the laser elements that can beincorporated in a single laser light source device, which in turn limitsthe increase in the optical output. Moreover, in some cases a metal filmis disposed on the surface of the reflection grating to improve thereflectance of the reflection grating. However, absorption of light bythe metal film cannot be completely eliminated, which may contribute toan increase of heat generation of the reflection grating due toabsorption of light at high output power. Such heat generation wouldreduce the reliability of the diffraction grating. In order to reducesuch heat generation, an improvement is required not only to thediffraction grating but also to the entire laser light source device inwhich the reflection grating is incorporated. In other words, such heatgeneration would lead degradation of performance and reliability of theWBC laser light source device. Whereas, a transmission grating is madeof a transparent material and such degradations caused by heatgeneration can be avoided, though optical loss due to mirror surfacereflection is greater in a transmission grating than that in areflection grating. In other words, a transmission grating exhibitslower diffraction efficiency.

Further, because a single diffraction grating, either a conventionaltransmission grating or a conventional reflection grating, requiresmicroscopic blazes to be formed in the surface, production of largequantities of diffraction gratings at a low production cost have beendifficult.

Accordingly, an object of certain embodiments of the present inventionis to provide a transmission grating with high diffraction efficiencythat can be mass produced at low cost, and a method of producing thesame.

A transmission grating according to one embodiment of the presentdisclosure has a flat light-incident surface and a flat light-emittingsurface, and includes a plurality of first light-transmissive regionshaving a refractive index of n₁ and a plurality of secondlight-transmissive regions having a refractive index of n₂ that issmaller than n₁. The first light-transmissive regions and the secondlight-transmissive regions are alternately disposed at a diffractiongrating period of d, where adjacent regions have an interfacetherebetween.

Among a plurality of interfaces between the first light-transmissiveregions and the second light-transmissive regions, light-reflectinginterfaces on which light transmitted through the firstlight-transmissive regions is made incident are in parallel with oneanother and also inclined such that a line normal to each of thelight-reflecting interfaces is at an inclination angle θ (0°<θ<90°) withrespect to the flat light-incident surface and to the flatlight-emitting surface.

When a thickness of the first light-transmissive regions in a directionperpendicular to the light-reflecting surfaces is t₁ and a thickness ofthe second light-transmissive regions in a direction perpendicular tothe light-reflecting surfaces is t₂, the thickness t₂, in μm, is in arange of 0.1/π(n₁ ²−n₂ ²)^(1/2) to t₁.

A method of producing a transmission grating according to one embodimentof the present disclosure includes: providing two glass plates eachhaving a first main surface and a second main surface located oppositeto the first main surface, the first main surface defining a pluralityof elongated reverse trapezoidal grooves of reverse trapezoidal shape ina vertical cross-section, each defined by a first wall, a second wall,and a bottom surface, with an upper opening width a, a bottom width b,and a depth h. The first walls of the elongated reverse trapezoidalgrooves are in parallel to one another and the second walls of theelongated reverse trapezoidal grooves are in parallel to one another,and the elongated reverse trapezoidal grooves are formed at an uniforminterval of (a+b−d1), thus providing a plurality of elongatedtrapezoidal protrusions each having trapezoidal cross-section with afirst wall and a second wall between adjacent elongated reversetrapezoidal grooves; engaging the elongated trapezoidal protrusions ofone of the two glass plates with the elongated reverse trapezoidalgrooves of the other of the two glass plates to fit the two glass platesto each other; and closely fitting the walls of one side of theelongated trapezoidal protrusions with the walls of one side of theelongated reverse trapezoidal grooves, closely fitting the uppersurfaces of the elongated trapezoidal protrusions with the bottomsurfaces of the elongated reverse trapezoidal grooves, and bonding toeach other.

A method of producing a transmission grating according to one embodimentof the present disclosure includes: stacking a plurality of thin glassplates of a same thickness with a predetermined space between each twoadjacent thin glass plates to obtain a multi-layered glass structure inwhich each two adjacent thin glass plates are facing each other acrossthe space; fusing a glass on each lateral surface of the multi-layeredglass structure to confine the spaces in the multi-layered glassstructure; supporting the multi-layered glass structure with the sealedspaces by a glass support structure, at an upper surface, a lowersurface, and two lateral surfaces opposite to each other with respect toa central axis that is parallel to the upper surface and the lowersurface of the multi-layered structure; heating the multi-layered glassstructure together with the glass support structure to collectivelysoften, and drawing the multi-layered glass structure and the glasssupport structure in a direction parallel to the central axis; andcutting the drawn multi-layered glass structure together with the drawnglass support structure in a direction parallel to a second planeperpendicular to a first plane including the central axis and a stackingdirection of the thin glass plates.

A method of producing a transmission grating according to one embodimentof the present disclosure includes: providing a plurality of thin glassplates of a same thickness, each having a first main surface, a secondmain surface opposite to the first main surface, a first lateralsurface, a second lateral surface, a third lateral surface, and a fourthlateral surface; the first main surface of each of the thin glass platesdefining a plurality of grooves with a predetermined opening width andrespectively extending from the first lateral surface side to the thirdlateral surface side, where the first lateral surface and the thirdlateral surface are located opposite to each other; stacking theplurality of thin glass plates such that openings of the grooves at thelateral end faces are arranged in a predetermined aligning direction toassemble a multi-layered glass structure; fusing an end surface portionof the multi-layered glass structure that includes the first lateralsurface of the thin glass plates, an end surface portion of themulti-layered glass structure that includes the second lateral surfaceof the thin glass plates, an end surface portion of the multi-layeredglass structure that includes the third lateral surface of the thinglass plates, and an end surface portion of the multi-layered glassstructure that includes the fourth lateral surface of the thin glassplates, to bond adjacent thin glass plates and also seal the openingends of the grooves; supporting the multi-layered glass structurecontaining the sealed grooves by a glass support structure, at the uppersurface, the lower surface, the end surface containing the secondlateral surfaces of the thin glass plates, and the end surfacecontaining the fourth lateral surfaces of the thin glass plates andlocated opposite to the end surface containing the second lateralsurfaces with respect to the central axis; heating the multi-layeredglass structure together with the glass support structure tocollectively soften, and drawing the multi-layered glass structure andthe glass support structure in a direction parallel to the central axis;cutting the drawn multi-layered glass structure together with the drawnglass support structure in a direction parallel to a first plane that isperpendicular to the central axis; and further cutting the multi-layeredglass structure and the drawn glass support structure in a directionparallel to a second plane that is in parallel to the predeterminedaligning direction of the grooves.

According to one aspect of the present invention, a transmission gratingwith high diffraction efficiency that can be mass produced at low costscan be provided. According to another aspect of the present invention, amethod of producing a transmission grating with high diffractionefficiency that can be mass produced at low costs can be provided.According to another aspect of the present invention, a laser devicethat includes the transmission grating with high diffraction efficiencyaccording to certain embodiments and that that can be mass produced atlow costs can be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic diagram illustrating a perspective view of atransmission grating according to a first embodiment.

FIG. 1B is a schematic diagram illustrating a side view of a firstlight-transmissive region of the transmission grating shown in FIG. 1A.

FIG. 1C is a schematic diagram illustrating a side view of a secondlight-transmissive region of the transmission grating shown in FIG. 1A.

FIG. 2 is a schematic diagram illustrating a cross-section of thetransmission grating shown in FIG. 1.

FIG. 3 shows the transmission grating according to the first embodiment,illustrating a first-order transmitted diffracted light with adiffraction angle of zero.

FIG. 4 is a diagram illustrating a minimum thickness of the transmissiongrating shown in FIG. 3.

FIG. 5 is a diagram illustrating a maximum thickness of the transmissiongrating shown in FIG. 3.

FIG. 6 is a schematic diagram of a laser light source device using thetransmission grating of the first embodiment.

FIG. 7 is a schematic diagram of a cross-section of a transmissiongrating according to a variational example 1 of the first embodiment.

FIG. 8 is a schematic diagram of a cross-section of a transmissiongrating according to a variational example 2 of the first embodiment.

FIG. 9A is a schematic diagram of a cross-section of a portion of atransmission grating according to a second embodiment.

FIG. 9B is a schematic diagram of a cross-section of a part of thetransmission grating according to the second embodiment.

FIG. 10A is a schematic diagram illustrating a zero-order reflected anddiffracted light in the transmission grating of variational example 1 ofthe first embodiment.

FIG. 10B is a schematic diagram of a cross-section illustrating aconfiguration to increase intensity of first-order reflected anddiffracted light in the transmission grating of the variational example1 of the first embodiment.

FIG. 10C is a schematic diagram of a cross-section illustrating aconfiguration to increase intensity of second-order reflected anddiffracted light in the transmission grating of the variational example1 of the first embodiment.

FIG. 11A is a schematic diagram of a cross-section of a glass plateformed with elongated trapezoidal protrusions in a method of producing atransmission grating according to a third embodiment of the presentinvention.

FIG. 11B is a schematic diagram of a cross-section illustrating twoglass plates respectively formed with elongated trapezoidal protrusionsare engaged to each other in the method of producing the transmissiongrating according to the third embodiment.

FIG. 11C is a schematic diagram of a cross-section illustrating twoglass plates respectively formed with elongated trapezoidal protrusionsand are engaged and fused to each other in the method of producing thetransmission grating according to the third embodiment.

FIG. 11D is a schematic diagram of a cross-section illustratingdiffraction of light beams in the transmission grating according to thethird embodiment.

FIG. 12A is a schematic perspective view illustrating spacer particlesscattered on a thin glass plate in the method of producing thetransmission grating according to a fourth embodiment of the presentinvention.

FIG. 12B is a schematic perspective view illustrating another thin glassplate placed on the spacer particles scattered on a thin glass plate inthe method of producing the transmission grating according to a fourthembodiment.

FIG. 12C is a schematic perspective view illustrating a multi-layeredglass structure assembled by stacking a predetermined number of thinglass plates on one another, in the method of producing the transmissiongrating according to the fourth embodiment.

FIG. 12D is a schematic perspective view illustrating sealing of themulti-layered glass structure in a method of producing the transmissiongrating according to the fourth embodiment.

FIG. 12E is a schematic cross-sectional view taken along line A-A ofFIG. 12D.

FIG. 12F is a schematic cross-sectional view taken along B-B of FIG.12D.

FIG. 13 is a schematic cross-sectional view illustrating the supportingof the sealed multi-layered glass structure by the glass supportstructure in the method of producing the transmission grating accordingto the fourth embodiment.

FIG. 14 is a schematic cross-sectional view illustrating the sealedmulti-layered glass structure being supported by the glass supportstructure, prior to drawing, in the method of producing the transmissiongrating according to a fourth embodiment.

FIG. 15 is a schematic cross-sectional view illustrating the sealedmulti-layered glass structure being supported by the glass supportstructure, after drawing, in the method of producing the transmissiongrating according to the fourth embodiment.

FIG. 16A is a schematic cross-sectional view illustrating the locationto cut the multi-layered glass structure and the glass support structureafter drawing, in the method of producing a transmission gratingaccording to the fourth embodiment.

FIG. 16B is a diagram schematically showing a cut surface obtained bycutting the multi-layered glass structure and the glass supportstructure, in the method of producing a transmission grating accordingto the fourth embodiment.

FIG. 17A is a schematic perspective view of a thin glass plate definingan array of periodic grooves in the method of producing a transmissiongrating according to a fifth embodiment.

FIG. 17B is a schematic perspective view of a stack of a plurality ofthin glass plates each defining a plurality of grooves, in the method ofproducing the transmission grating according to the fifth embodiment.

FIG. 17C is a schematic perspective view illustrating a thin glass plateabsent of grooves placed on a stack of a plurality of thin glass plateseach defining a plurality of grooves, in the method of producing thetransmission grating according to the fifth embodiment.

FIG. 17D is a schematic perspective view illustrating the stack of theplurality of thin glass plates being fused together, in the method ofproducing the transmission grating according to the fifth embodiment.

FIG. 17E is a schematic cross-sectional view taken along line A-A ofFIG. 17D.

FIG. 18 is a schematic cross-sectional view illustrating themulti-layered glass structure supported by the glass support structurein the method of producing the transmission grating according to thefifth embodiment.

FIG. 19A is a schematic perspective view illustrating a cut surfaceobtained by cutting the drawn multi-layered glass structure togetherwith the support structure, in a direction parallel to a planeperpendicular to the drawing direction.

FIG. 19B is a schematic cross-sectional view illustrating cutting thecut product of the multi-layered glass structure and the supportstructure shown in FIG. 19A, along a plane parallel to the drawingdirection.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Certain embodiments according to the present invention will be describedbelow with reference to the accompanying drawings. It is to be notedthat the light emitting device described below is intended forimplementing the technical concepts of the present invention, and thepresent invention is not limited to those described below unlessotherwise specified. Also, descriptions of one embodiment and/or oneexample can be applied to other embodiments and/or other examples. Inthe description below, the same designations or the same referencenumerals refer to same or like members, and duplicative descriptionswill be appropriately omitted. The size, positional relationship and thelike in the drawings may be exaggerated for the sake of clarity.

First Embodiment

A transmission grating according to a first embodiment of the presentinvention will be described below.

The transmission grating according to the first embodiment is of avolume phase diffraction grating. As shown in FIGS. 1A-1C, thetransmission grating according to the first embodiment includes aplurality of first light-transmissive regions 10 each having arefractive index of n₁ and a plurality of second light-transmissiveregions 20 each having a refractive index of n₂ that is smaller than thefirst refractive index n₁, alternately arranged between a flatlight-incident surface 30 and a flat light-emitting surface 40. Each ofthe first light-transmissive regions 10 is a first rectangularparallelepiped member or region having two congruent parallelogrambases: a first base 15 and a second base 16, and four rectangularlateral surfaces: a first, second, third, and fourth lateral surfaces11, 12, 13, and 14 between the first base 15 and the second base 16. Thefirst lateral surface is located at a light-incident side, the secondlateral surface is located at a light-emitting side, the third lateralsurface is located at a first light-reflecting interface, and the fourthlateral surface is located at a second light-reflecting interface, to bedescribed below. Each of the second light-transmissive regions 20 is asecond rectangular parallelepiped member or region having two congruentparallelogram bases: a first base 25 and a second base 26, and fourrectangular lateral surfaces: a first, second, third, and fourth lateralsurfaces 21, 22, 23, and 24 between the first base 25 and the secondbase 26. One opposite angles of the first base 15 and the first base 25are 90°−θ and the other opposite angles of the first base 15 and thefirst base 25 are 90°+θ. The length of one pair of opposite sides of thefirst base 15 of the first light-transmissive region 10 is equal to thelength of one pair of opposite sides of the first base 25 of the secondlight-transmissive region 20. In other words, the third and fourthlateral surfaces 13, 14 of each of the first light-transmissive regions10 and the third and fourth lateral surfaces 23, 24 of each of thesecond light-transmissive regions 20 are all congruent. In theconfiguration described above, the first and second lateral surfaces 11,12 of the first light-transmissive regions 10 and the first and secondlateral surfaces 21, 22 of the second light-transmissive regions 20 aresuch that at least the long sides of the first and second lateralsurfaces 11, 12 and the long sides of the first and second lateralsurfaces 21, 22 have a same length and each of adjacent first lateralsurface 11 and the first lateral surface 21 share a single long side,and each of adjacent second lateral surface 12 and the second lateralsurface 22 share a single long side.

A plurality of the first rectangular parallelepipeds (the firstlight-transmissive regions 10) and a plurality of the second rectangularparallelepipeds (the second light-transmissive regions 20) as describedabove are alternately arranged to form the transmission grating of thefirst embodiment. At this time, (i) the first lateral surfaces 11 andthe first lateral surfaces 21 are located on a same plane and thelateral surface 12 and the lateral surface 22 are located on a sameplane, and also (ii) each of two adjacent lateral surfaces of the thirdlateral surface 13 and the fourth lateral surface 24 are in contact witheach other and each of two adjacent lateral surfaces of the fourthlateral surface 14 and the third lateral surface 23 are in contact witheach other. In the transmission grating of the first embodiment, thefirst lateral surfaces 11 and the first lateral surfaces 21 located on asame plane constitute a flat light-incident surface 30, and the secondlateral surfaces 12 and the second lateral surfaces 22 located on a sameplane constitute a flat light-emitting surface 40.

The transmission grating of the first embodiment with a configurationdescribed above has a plurality of surfaces where two adjacent lateralsurfaces of the fourth lateral surface 14 and the third lateral surface23 are in contact with each other (creating interfaces between the firstlight-transmissive regions 10 and the second light-transmissive regions20), each constituting a first light-reflecting interface 27 where lighttransmitted through the first light-transmissive region is incident andreflected. A line normal to the first light-reflecting interface 27 isinclined at an inclination angle θ (0°<θ<90°) to the flat light-incidentsurface 30 and the flat light-emitting surface 40. A normal vectorpointing from the first light-reflecting interface 27 toward the firstlight-transmissive region 10 side is directed to the flat light-emittingsurface. The inclination angle θ in a range of greater than 0° and equalor smaller than 45° is suitable for a transmission grating. Theplurality of first light-reflecting interfaces 27 are in parallel to oneanother. The distance between two adjacent light-reflecting interfaces27 on the flat light-incident surface or the flat light-emitting surfaceis the diffraction grating period d of the transmission grating of thefirst embodiment. That is, as shown in FIG. 2, the diffraction gratingperiod d is a sum of widths of two adjacent lateral surfaces 11 and 21.

When a thickness of the first light-transmissive regions in a directionperpendicular to the first light-reflecting interfaces 27 is t₁ and athickness of the second light-transmissive regions in a directionperpendicular to the light-reflecting surfaces is t₂, the thickness t₀of the second light-transmissive region 20, in μm, is preferably in arange of 0.1/π(n₁ ²−n₂ ²)^(1/2) to t₁. The thickness t₁ of the firstlight-transmissive region is determined as a product of the width of thefirst lateral surface 11 and cosine of inclination angle θ (cos θ). Thethickness t₀ of the second light-transmissive region 20 is determined asa product of the width of the first lateral surface 21 and cosine ofinclination angle θ (cos θ).

The transmission grating of the first embodiment will be described indetail below.

In the description below, the distance between the flat light-incidentsurface 30 and the flat light-emitting surface 40 is indicated as adiffraction grating region thickness t. The plurality of firstlight-transmissive regions 10 are made of a first transparent materialhaving a refractive index n₁. The plurality of second light-transmissiveregions 20 can be made of a second transparent material having arefractive index n₂ (1≤n₂<n₁) or, alternatively, may be formed by aliquid, a vacuum whose refractive index is 1, or a gas that has arefractive index of approximately 1. The refractive index n₁ may bereferred to as “high refractive index n₁”, and the refractive index n₂may be referred to as “low refractive index n₂” in the descriptionbelow. When a material has a refractive index n, a thickness T, and anoptical absorption coefficient α, the transmittance to light from avacuum perpendicularly incident on two parallel plates made of thematerial can be expressed as (1−R)²e^(−αT), where e is the base ofnatural logarithm, R is a reflectance of light perpendicularly incidenton a material having a refractive index of n in vacuum. In the presentspecification, the term “(a) transparent material” refers that thematerial has an internal transmittance e^(−αT) of 0.9 or greater, morepreferably 0.99 or greater. For example, the optical absorptioncoefficient α of the material is preferably 0.01 cm⁻¹ or less, morepreferably 0.001 cm⁻¹ or less. Further preferably, the imaginarycomponent of the refractive index n_(j) (j is zero or a positiveinteger; j=1, 2, . . . ) of the material can be assumed zero and thematerial exhibits substantially no absorption of light (i.e., absorptionof light in the material with a thickness t can be negligible). When theabsorption of light by the material is negligible, heat generation inthe material due to absorption of light can be negligible even when theoptical density is increased. Thus, reliability of the diffractiongrating that employs the material and the light source device thatemploys the diffraction grating can be improved.

The first transparent material and the second transparent material arepreferably inorganic materials. Because, inorganic materials generallyhave superior light-resisting properties than organic materials. Forexample, an optical glass such as a synthetic quartz glass, aborosilicate crown glass known as BK7 can be used for the firsttransparent material. For the second transparent material, for example,an optical glass such as a synthetic quartz glass, a borosilicate crownglass known as BK7 can be used or, alternatively, vacuum, air, nitrogengas, a rare gas, or the like, can be used. Further, depending on thewavelength to diffract, an elemental semiconductor such as silicon orgermanium, a compound semiconductor such as ZnS, GaAs, or GaN, a metaloxide such as sapphire, gallium oxide, zinc oxide, or hafnium oxide, orother material, such as a dielectric material can be used as the firsttransparent material and/or the second transparent material.

As described above, a line normal to the first light-reflectinginterface 27 is inclined at an inclination angle of θ to the flatlight-incident surface 30 and the flat light-emitting surface 40. In thetransmission grating of the first embodiment, the inclination angle θcan be in a range of 0°≤θ<90°, but the inclination angle θ in a range of0°≤θ<45° is preferable.

In the transmission grating of the first embodiment, the light passingthrough the first light-transmissive region 10 and reflected from thefirst light-reflecting interface 27 is used as the transmitteddiffracted light. Accordingly, when t₁ is greater than t₂, a greateramount of light is allowed to pass the first light-transmissive region10. Thus, in order to increase the amount of light reflected at thefirst light-reflecting interface 27 and increase the diffractionefficiency, a greater t₁ than t₂ is preferable.

The operation of a transmission grating according to the firstembodiment will be described in detain below, with reference to FIG. 3and FIG. 4.

In the description below, light having a wavelength λ in vacuum isassumed to be incident on the flat light-incident surface. In thefigures, incident light is oriented at an angle (incident angle) α to aline normal to the flat light-incident surface of the diffractiongrating region, and an m-order diffracted light is oriented at an angle(diffraction angle) βm (where m is an integer (0, ±1, ±2, . . . , orderof the diffraction) to a line normal to the flat light-emitting surface(or the flat light-incident surface) of the diffraction grating region.In the case of a plurality of different wavelengths of incident light,λ_(i) denotes the wavelength in vacuum of incident light i, α_(i)denotes the angle (the incident angle) between the incident light i andthe normal to the flat light-incident surface of diffraction gratingregion, where i is an integer. In the description below, θ is in a rangeof 0° to 45° (FIGS. 1A-1C, FIG. 2).

In the transmission grating shown in FIG. 2, the diffraction gratingperiods d, and t₁, t₂, and θ satisfy the relationship (1).d=(t ₁ +t ₂)/cos θ  (1)

FIG. 3 illustrates an incident light entering the transmission grating100 shown in FIG. 2, at an incident angle α₀ to the flat light-incidentsurface 30, from a space with a refractive index n₀. As illustrated inFIG. 3, light 50 incident on the first light-transmissive region 10 witha refractive index n₁, in the flat light-incident surface 30 (firstlateral surface 11) at an angle of incidence α₀, propagates in the firstlight-transmissive region 10 at an angle of refraction α₁. According toSnell's law, n₀, α₀, n₁, and α_(i) satisfy the relationship (2).n ₁ sin α₁ =n ₀ sin α₀  (2)

The incident light to the transmission grating 100 is reflected at thefirst light-reflecting interface 27. In this case, according to the lawof reflection, the angle of incidence and the angle of reflection to thefirst light-reflecting interface 27 are equal. The reflected light istransmitted through the first light-transmissive region 10 and emittedfrom the flat light-emitting surface (second lateral surface 12). In thetransmission grating 100, light 50 incident on the firstlight-transmissive region 10 through the flat light-incident surface 30is reflected at the first light-reflecting interface 27 and emitted fromthe flat light-emitting surface 40, and diffraction light occurs in thedirection where the reflected light emitted from the flat light-emittingsurface 40 satisfies the diffraction condition for m^(th)-order (i.e.,the difference in optical paths is an integer multiple (m times) ofwavelength). In the first embodiment, the diffracted light is assumed tobe emitted from the flat light-emitting surface 40 into a vacuum. Whend(sin α−sin βm)=mλ, where m≠0 is satisfied in a vacuum, the intensity ofthe m^(th)-order transmitted diffracted light increases. In thetransmission grating 100, the first light-reflecting interfaces 27 arealso provided, aiming to eliminate straight forward propagation of theincident light incident from the flat light-incident surface (the firstsurface 11 of the first light-transmissive region 10) so that zero-ordertransmitted diffracted light can be suppressed. In the transmissiongrating 100 of the first embodiment, it is preferable to set thethickness t of the transmission grating and the thickness t₁ of thefirst light-transmissive region so that light incident from the flatlight-incident surface (the first lateral surface 11 of the firstlight-transmissive region 10) is not emitted from the flatlight-emitting surface 40 as a zero-order transmitted diffracted light.

In the transmission grating 100, first-order diffracted light that hasgreater intensity than second or higher order diffracted light ispreferably used, in which, the first light-reflecting interface 27 ispreferably a flat surface similar to a mirror surface. Morespecifically, the light-reflecting interface preferably has a surfaceaccuracy (in other words, a flatness or a flatness degree) of λ/4 orless, more preferably λ/8 or less. Because, the closer to a mirrorsurface, the larger reduction of scattering light, and which can reducethe second-order transmitted diffracted light.

Next, an example of the transmission grating of the first embodimentwill be described, in which the zero-order transmitted diffracted lightis reduced or eliminated and intensity of the first-order transmitteddiffracted light is used. In the example shown below, description willbe given mainly with reference to FIG. 3, on the case in which thefirst-order diffraction angle of transmitted light is zero. In thedescription below, a transmission grating according to the firstembodiment using intensity of first-order transmitted diffracted lightwill be described, but the transmission grating according to the firstembodiment can also be structured by using diffracted light of higherorder such as a second-order or third-order diffracted light.

As illustrated in FIG. 3, when two adjacent incident lights enter theflat light-incident surface 30 at locations spaced apart from each otherat a distance d that is a diffraction grating period, the difference inoptical paths is d sin α₀. In the case of a transmission grating, thediffraction condition for first-order requires that the difference inoptical paths is equal to the wavelength in the material the twoadjacent incident lights propagate. The example shown in FIG. 3satisfies the equation (3).d sin α₀ =λ/n ₀  (3)

Further, in the present example, light reflected at the firstlight-reflecting interface 27 propagates in a direction perpendicular tothe flat light-emitting surface 40 (i.e., β₁=0). Thus, the angle ofrefraction α₁.is equal to twice the incident angle θ (i.e., α₁=2θ).

From the equations (1), (2), (3), and α₁=2θ, λ, n1, t1, t2 and θ satisfythe equation (4-1) or (4-2).λ/(t ₁ +t ₂)=2n ₁ sin θ  (4-1)orθ=arcsin(λ/2n ₁(t ₁ +t ₂))  (4-2)

As described above, by alternatively stacking the firstlight-transmissive region 10 having a thickness of t₁ and the secondlight-transmissive region 20 having a thickness of t₂ at an inclinationangle θ that satisfies the equation (4-1) or (4-2), the transmissiongrating 100 that can enhance the intensity of first-order transmitteddiffracted light 61 can be obtained.

Next, the thickness t of the transmission grating 100 will be describedwith reference of FIG. 4.

If the thickness t of the transmission grating 100 is too small, theamount of zero-order transmitted diffracted light, that is, the amountof the incident light that is not reflected at the firstlight-reflecting interface 27 but is transmitted through the firstlight-transmissive region 10 will increase. Therefore, the thickness tof the transmission grating 100 is preferably set so as not increase theamount of zero-order transmitted diffracted light. More specifically, inorder to reduce or eliminate light transmit through the firstlight-transmissive region 10 without being reflected at the firstlight-reflecting interface 27, the minimum value t_(min) of thethickness t of the transmission grating 100 can be given in the equation(5).t _(min) =t ₁ cos 2θ/sin θ  (5)

FIG. 4 illustrates a schematic of the operation of the transmissiongrating 100 with the minimum thickness t_(min). As shown in FIG. 4, whenthe thickness t of the transmission grating 100 is smaller than theminimum thickness t_(min), a portion of the incident light may betransmitted through the first light-transmissive region 10 without beingreflected at the light-reflecting interfaces.

Meanwhile, when the thickness t of the transmission grating 100 is toolarge, light reflected at the first light-reflecting interface 27 maypropagate in the first light-transmissive region 10 and is reflected atthe second light-reflecting interface 28 at the opposite side of thefirst light-reflecting interface 27, which increases the zero-orderdiffracted light. The second light-transmissive region 28 is theinterface between a fourth lateral surface 14 of the firstlight-transmissive region 10 and a third lateral surface 23 of thesecond light-transmissive region 14. Reflection of light at the secondlight-reflecting interface 28 may increase optical loss such asscattering loss and therefore undesirable. The maximum value (t_(max))of the thickness t of the transmission grating 100, which allows lightreflected at the first light-first reflecting interface 27 to betransmitted from the flat light-emitting surface 40 without beingreflected at the second light-reflecting interface 28 can be determinedfrom the equation (6).t _(max) =t ₁/sin θ  (6)

FIG. 5 illustrates a schematic of the operation of the transmissiongrating 100 with the maximum thickness t_(max). As shown in FIG. 5, whenthe thickness t of the transmission grating 100 is larger than themaximum thickness t_(max), light may be reflected at the secondlight-reflecting interface 28.

As can be seen from the description above, the thickness t of thetransmission grating 100 preferably satisfy the relation of (7)t ₁ cos 2θ/sin θ<t<t ₁/sin θ  (7)

As described above, when the transmission grating 100 has a thickness tthat satisfies the equation (7), incident light to the firstlight-transmissive region 10 can be reflected at the firstlight-reflecting interface 27 and transmitted from the flatlight-emitting surface 40 without being reflected at the secondlight-reflecting interface 28, and further, transmission of zero-ordertransmitted diffracted light from the flat light-emitting surface 40 canbe controlled. Accordingly, a transmission grating of high diffractionefficiency, capable of diffracting only first-order transmitteddiffracted light can be formed.

The transmission grating 100 having such a structure as described abovecan be produced by, for example, alternatively stacking a plurality oftransparent plates (thickness t₁) of a high-refractive index (n₁) forthe first light-transmissive regions 10 and a plurality of transparentplates (thickness t₂) of a low-refractive index (n₂) for the secondlight-transmissive regions 20, joining them to form a stacked-platestructure, then, tilting the stacked-plate structure at an angle θ,which satisfies the equation (4-1) or (4-2), with respect to the linenormal to the plane, cutting the tilted stacked-plate structure in thenormal direction and at two parallel planes having a distance satisfyingthe equation (6) that is approximately the maximum thickness t_(max),then polishing to a thickness t satisfying the equation (7). Morespecific method of producing such a transmission grating 100 will bedescribed further below.

Next, the thickness t of the transmission grating 100, the thickness t₁of the first light-transmissive region 10, and the thickness t₂ of thesecond light-transmissive region 20 will be described in detail.

When the tilting angle θ is in a range of 0≤θ<45°, the maximum thicknesst_(max) of the thickness t of the transmission grating 100 monotonicallydecreases as the tilting angle θ increases, as indicated in the equation(8). Equation (8) is obtained by substituting the formula given in (4-2)into the formula given by (6).t _(max)=2n ₁ t ₁(t ₁ +t ₂)/λ  (8)

The equation (8) indicates that when a wavelength λ and a highrefractive index n1 of the incident light 50 are given, the greater thevalue of t₁(t₁+t₂), the greater the thickness t can be. With a greaterthickness t, mechanical strength of the transmission grating 100 can beincreased. However, when the sum of the thicknesses (t₁+t₂) of the firstlight-transmissive region 10 and the second light-transmission region 20is too large, the number of allowed diffraction orders increases, whichwould increase stray light. Accordingly, in the transmission grating 100of the first embodiment, a greater value of t₁(t₁+t₂) is preferablewithin a range where the incident angle α₀ satisfying α₀>30°.

Next, the incident angle α₀ will be described. The equations (1) and (3)and the diffraction condition lead to the equation (9).sin β_(m)=(1−m)λ cos θ/n ₀(t ₁ +t ₂)  (9)

Also, from the relationship: |sin β_(m)|≤1, the relationship (10) isgiven.−1≤(1−m)λ cos θ/n ₀(t ₁ +t ₂)≤1  (10)

Because |cos θ|≤1, the equation (10) indicates that the greater value of(t₁+t₂), a wider range of values that m is allowed. That is, the moreorders of diffraction are allowed. The use of a diffraction grating thatallows multiple orders of diffraction in a light source device wouldincrease the amount of light that does not involve the optical output ofthe light source device. Therefore, setting of (t₁+t₂) too great invalue is not desirable.

For this reason, for example, the incident angle α₀ is preferably set ina range satisfying the inequality (11).0.5<λ cos θ/n ₀(t ₁ +t ₂)=sin α₀  (11)

When the inequality (11) is satisfied, the integers m allowed in therelationship (10) are limited to 0, 1, and 2, which give the diffractionangles of α₀, 0, and −α₀, respectively. Accordingly, the incident angleα₀ is preferably set to satisfy the relationship (11), that is, to setin a range of 90°>α₀>30°.

Next, incident light to the transmission grating 100 will be illustratedusing a linearly polarized laser light such as laser light emitted froman edge-emitting semiconductor laser. When a p-polarized light isincident on the transmission grating 100 from a space with a refractiveindex of n₀, the reflectance at the interface between the space of therefractive index n₀ and the first light-transmissive region 10 becomeszero at a certain angle of incidence (i.e., Brewster's angle θ_(B)). Inthis case, the incident angle α₀ is more preferably set in a range of30°≤α₀≈θ_(B). Because, the incident angle α₀ greater than Brewster'sangle θ_(B) leads to a rapid increase in the amount of light reflectedat the interface between the space of the refractive index n₀ and thefirst light-transmissive region 10 (i.e., a first lateral surface 11 ofthe first light-transmissive region 10 in the flat light-incidentsurface. The incident angle α₀ is further preferably set to Brewster'sangle θ_(B). Because, with this angle, reflection of light at the firstlateral surface 11 of the first light-transmissive region 10 in the flatlight-incident surface is eliminated, and thus, a reduction in thezero-order reflected and diffracted light can be obtained. That is, ofthe light reflected from the interface between the space of therefractive index n₀ and the first lateral surfaces 11, 21 of the firstlight-transmissive region 10 (i.e., the first lateral surface 11 of thefirst light-transmissive region 10) is eliminated, and the lightreflected from the interface between the space of the refractive indexn₀ and the second light-transmissive region 20 (i.e., the first lateralsurface 21 of the second light-transmissive region 20) remain.Brewster's angle θ_(B).is defined by the equation (12).tan θ_(B) =n ₁ /n ₀  (12)

When n₀=1, then θ_(B)>45°, where θ_(B)=α₀>30° is always satisfied. Thus,the number of allowed diffraction orders can be limited to 0, 1, and 2.

When α₀=θ_(B), from the equations (2), (12), and α₁=2θ, the relationshipbetween n₀, n₁, and θ satisfy the equation (13).θ=arcsin(cos(arctan(n ₁ /n ₀)))/2  (13)

From the equations (13) and (7), the thickness t of the transmissiongrating 100 satisfies the relationship (14). Further, when a wavelengthλ is given, the equations (13) and (4-1) give the equation (15).t ₁ sin(arctan(n ₁ /n ₀))/sin(arcsin(cos(arctan(n ₁ /n ₀)))/2)<t<t₁/sin(arcsin(cos(arctan(n ₁ /n ₀)))/2)  (14)t ₁ +t ₂=λ/2n ₁ sin(arcsin(cos(arctan(n ₁ /n ₀)))/2)  (14)

When the first light-transmissive regions 10 each having a thickness oft₁ and the second light-transmissive regions 20 each having a thicknessof t₂, satisfying the relation (14) are alternatively stacked at atilting angle θ satisfying the equation (13) to structure thetransmission grating 100 whose thickness t satisfying the relationship(14), the transmission grating 100 has a diffraction grating period ofλ/n₁ cos(arctan(n₁/n₀)). When a p-polarized light is incident atBrewster's angle θ_(B) on the transmission grating 100 structured asdescribed above, zero-order reflected and diffracted light andzero-order transmitted diffracted light can be reduced, and third orhigher-order diffracted light can be eliminated, whereas the intensityof the first-order transmitted diffracted light 61 can be enhanced.

The reflectance of light with an incident angle smaller than Brewster'sangle θ_(B) gives a smaller reflectance. Thus, if the incident angle α₀is cannot be set to Brewster's angle θ_(B), an incident angle that issmaller than Brewster's angle θ_(B) is preferably selected. When theincident angle α₀ is smaller than Brewster's angle θ_(B), using a knownmethod to form an antireflection layer of a single-layer or multilayerdielectric film on the flat light-incident surface of the transmissiongrating can reduce the reflected and diffracted light.

When a s-polarized light is incident from the space of the refractiveindex n₀ on the transmission grating 100, an incident angle that gives areflectance of zero is not present. In this case, an increase of theincident angle α₀ leads to a monotonic increase of the reflectance atthe side surface 11 of the first light-transmissive region. Thus, theincident angle α₀ is preferably set to slightly greater than 30°.

Next, the high refractive index n₁, the low refractive index n₂, and thetilting angle θ will be discussed. The incident angle to the firstlight-reflecting interface 27 can be expressed as 90°−α₁+θ. When α₁=2θ,the incident angle is 90°−θ.

Because n₂<n₁, there is a critical angle θ_(c) of incidence. When theincident angle to the first light-reflecting interface 27 is greaterthan the critical angle θ_(c), the incident light is totally internallyreflected. When the equation (16) is satisfied, total internalreflection takes place. Thus, zero-order transmitted diffracted lightcan be reduced and the intensity of the first-order transmitteddiffracted light 61 can be enhanced, and therefore preferable.90°−θ>θ_(c)=arcsin(n ₂ /n ₁)  (16)

That is, the smaller the tilting angle θ, the larger the selection ofmaterials for the first light-transmissive region 10 and the secondlight-transmissive region 20 that satisfy the conditions for totalinternal reflection. Also, the smaller n₂/n₁, the smaller the criticalangle θ_(c), allowing a wider range of tilt angle θ that allows totalinternal reflection, and therefore preferable. The refractive index ofthe gas is smaller than the refractive index of the liquid or the solid,therefore, a gas is preferably used as the second transparent material.Because, the refractive index n₂ of the second transparent material canbe closer the smallest value of 1. When a gas is used as the secondtransparent material, the first light-transmissive regions of a firsttransparent material are arranged at an interval of t₂, providingintervening second regions, and a gas is filled in the interveningsecond regions. In conditions of total internal reflection at the firstlight-reflecting interface 27, evanescent light is generated at theinterface 27 and penetrate into the second light-transmissive region 20.The penetration depth D of the evanescent light into the secondlight-transmissive region 20 is expressed by the equation (17).D=λ/4π((n ₁ sin(90°−θ))² −n ₂ ²)^(1/2)  (17)

When θ=0°, the depth D is the minimum value of λ/4π(n₁ ²−n₂ ²)^(1/2).When the thickness t₂ of the second light-transmissive region 20 issmaller than the penetration depth D, light propagates through thesecond light-transmissive region 20 into the adjacent firstlight-transmissive region 10, resulting in a decrease in the intensityof the first-order transmitted diffracted light 61 and an increase inthe optical loss due to zero-order transmitted diffracted light andinterface scattering. Thus, the thickness t₂ of the secondlight-transmissive region 20 is preferably greater than λ/4π(n₁ ²−n₂²)^(1/2). For the transmission gratings designed for visible light orinfrared, the wavelength λ is 0.4 μm or greater. Therefore, thethickness t₂ of the second light-transmissive region 20, in μm, ispreferably greater than 0.1/π(n₁ ²−n₂ ²)^(1/2). Further, when a gas isused as the second transparent material, n₂ ²≈1, and thus the thicknesst₂ of the second light-transmissive region 20, in μm, is preferablygreater than 0.1/πn₁ ². When α₁=2θ, the smaller the tilt angle θ, thesmaller the penetration depth D. Thus, light propagates in the secondlight-transmissive region 20 can be reduced, which increase theintensity of the first transmitted diffracted light 61, and thuspreferable. Further, the higher the refractive index n₁ of the firstlight-transmissive region 10, the smaller the penetration depth D, andtherefore preferable. For visible light or infrared, various kinds ofoptical glasses can be suitably used as the first and second transparentmaterials.

Next light incident on the first lateral surfaces 21 of the secondlight-transmissive regions 20 that constitute portions of the flatlight-incident surface will be discussed. The angle of refraction α₂incident on the first lateral surface 21 of the secondlight-transmissive region 20 satisfies the equation (18) according toSnell's Law.n ₂ sin α₂ =n ₀ sin α₀  (18)

Because n₂<n₁, there is no critical angle θ_(c). When α₂>α₁, theincident angle to the second light-reflecting interface 28 is smallerthan 90°−θ. Compared to the case where light incident on the firstlateral surface 11 of the first light-transmissive region 10 is incidenton the first light-reflecting interface 27, the second light-reflectinginterface 28 exhibits lower reflectance and higher transmittance. Theangle of light exiting from the flat light-emitting surface of thetransmission grating, after being incident on the first lateral surface21 of the second light-transmissive region 20 and is reflected once atthe second light-reflecting interface 28, is not zero. Thus, lightincident on the first lateral surface 21 of the secondlight-transmissive region 20 does not satisfy the conditions fordiffraction, and thus does not increase first-order transmitteddiffracted light 61. Also, when light is incident on the first lateralsurface 21 of the second light-transmissive region 20 and is transmittedand diffracted through the second light-transmissive region 28,first-order transmitted diffracted light 61 is not generated. That is,light incident on the first lateral surface 21 of the secondlight-transmissive region 20 becomes stray light that results in opticalloss. For this reason, in order to reduce light incident on the firstlateral surface 21 of the second light-transmissive region 20, a smallert₂/t₁ is preferable. Whereas, t₂ is greater than λ/4π(n₁ ²−n₂ ²)^(1/2).

Next, the reflectance R of light perpendicularly incident on the secondlateral surface 12 of the first light-transmissive region 10 will bedescribed. The reflectance R can be given by (19) below.R=(n ₁ −n ₀)²/(n ₁ +n ₀)²  (19)

That is, the second lateral surface 12 of the first light-transmissiveregion 10 serves as a partially transmissive mirror having a reflectanceof R, given by the equation (19). Further, providing a dielectricmultilayer film or a dielectric single film on the flat light-emittingsurface of the transmission grating 100 allows adjusting the reflectanceof the flat light-emitting surface of the transmission grating 100. Forexample, by adjusting the reflectance of the flat light-emitting surfaceof the transmission grating 100, the flat light-emitting surface of thetransmission grating 100 can be used in place of the partiallytransmissive mirror (partially reflecting mirror, retroreflectivemirror) of WBC (wavelength beam combining) system shown in FIG. 5 of“Laser Beam Combining for High-Power High-Radiance Sources” T. Y. Fan,IEEE Journal of Selected Topics in Quantum Electronics, Vol. 11, No. 3,May/June 2005, pp. 567-577. This can lead to a reduction of the numberof components of a laser light source device, stabilizing the positionalrelationship between the wavelength dispersive element and the partiallyreflecting mirror, and reducing time-dependent change, which cancontribute to improvement in the reliability of the WBC laser lightsource devices. The reflectance of the partially transmissive mirror isan important factor for the performance and reliability of the WBC laserlight source devices. Because, the reflectance of the partiallytransmissive mirror determines the feedback quantity of light to thelaser element, and stability of oscillation wavelength of the laserelement. Adjusting of the reflectance of the dielectric multilayer filmor dielectric single layer can be performed by using a known filmdeposition method.

FIG. 6 is a schematic diagram of a WBC laser light source device usingthe transmission grating 100 of the first embodiment. In the laser lightsource device shown in FIG. 6, a laser array 200 and an incident-sideoptical system (collimating lens) 310 are arranged at the flatlight-incident surface side of the transmission grating 100, and alight-emitting side optical system (condensing lens) 320 and an outputoptical fiber 400 are arranged at flat light-emitting surface side ofthe transmission grating 100.

In the laser light source device 500 shown in FIG. 6, the back endsurface of the laser array 200 and the transmission grating 100constitute an external resonator. Laser array 200 is configured to emita plurality of laser lights having different wavelengths λ_(i) (i is aninteger) with a predetermined divergence angle. Divergence angle of eachlaser light of the different wavelengths λ_(i) is reduced through thelight-incident side optical system (collimate lens) 310 to a divergenceangle of substantially zero to cause light ray groups. Each of the laserlights of different wavelengths λ_(i) in the light ray groups isincident on the flat light-incident surface of the transmission grating100 at an incident angle of α_(i). The refractive index n of the space,the diffraction grating period d, the wavelength λ_(i), and the incidentangle α_(i) satisfy the relationship d sin α₁=λ_(i)/n. That is, lightray groups having a wavelength λ_(i) and incident on the transmissiongrating 100 at an incident angle α₁ are superposed through thetransmission grating 100 and are emitted perpendicularly from the flatlight-emitting surface. The light ray groups emitted from the flatlight-emitting surface are condensed on an end surface of an outputoptical fiber 400 by the light-emitting side optical system (condensinglens) 320. At this time, second-order reflected and diffracted light ofeach of the laser lights of the light ray group having a wavelength eachof the laser lights and incident on the transmission grating 100 at anincident angle α_(i) is reflected in the reverse direction of theincident direction (retroreflective reflection). That is, thetransmission grating 100 and the back end surface of the laser array 200constitute a resonator structure. With the resonator structure (externalresonator structure) as described above, reliability of WBC laser lightsource devices can be improved. Change in the temperature of the laserarray 200 during its operation may change the wavelength λ_(i). Also,heat generated during the operation, and/or change in time may changethe incident angle α_(i). However, with the external resonator structureas described above, such a change in the wavelength λ_(i) can bereduced, and a change in the incident angle α_(i) leads toretroreflective reflection, which contribute to improving the stabilityof laser output power.

In order to realize higher optical output power with a laser lightsource device, an increase in the number of constituting components ofthe laser light source such as increasing the number of laser arrays,providing a polarizing prism to create a polarized wave, may berequired. However, with the use of the transmission grating 100according to the first embodiment, constituting components can bearranged separately at the flat light-incident surface side and the flatlight-emitting surface side of the transmission grating 100, allowingeasier placement of the constituting components compared to that withthe use of a reflection grating, and thus suitable for higher opticaloutput power of the laser light source device.

Next, variational examples according to the first embodiment will bedescribed.

Variational Example 1

The transmission grating 100 according to the first embodiment,operating at visible light wavelengths have a thickness t, for example,in a range of about 0.84 μm to about 1.87 μm, when the first transparentmaterial is a glass having a refractive index 1.51, and the secondtransparent material is the air, and light having a wavelength 0.5 μm isincident at an angle of 56.5°. When the thickness t of the transmissiongrating 100 is too small to have sufficient mechanical strength, a platemade of a transparent material and having substantially uniformthickness is preferably joined to the flat light-incident surface or theflat light-emitting surface of the transmission grating 100.

As shown in FIG. 7, the transmission grating 110A according to thevariational example 1 has a configuration similar to that of thetransmission grating 100 according to the first embodiment, except thata plate made of a transparent material and having a refractive index ofn₁ is provided to the flat light-incident surface and the flatlight-emitting surface of the transmission grating 100. Morespecifically, a first light-transmissive plate 111 having a refractiveindex of n₁ is integrally connected to the flat light-incident surface30, and a second light-transmissive plate 112 having a refractive indexof n₂ is integrally connected to the flat light-emitting surface plane40 of the transmission grating 100 corresponding to the firstembodiment. The bonding can be carried out by employing a known bondingmethod such as adhesion or welding, using a transparent adhesive.Further, a dielectric multilayer film or a dielectric single film can bedisposed on the outer surface (i.e., the surface that is opposite sideof the surface bonded to the transmission grating 100) of the secondlight-transmissive plate 112, to provide a predetermined partiallytransmissive mirror. The first light-transmissive region 10, the firstlight-transmissive plate 111, and the second light-transmissive plate112 may be produced in one body as described further below, instead ofthe method as described above, in which after the transmission grating100 according to the first embodiment is provided, the firstlight-transmissive plate 111 is bonded to the flat light-incidentsurface 30 and the second light-transmissive plate 112 is bonded to theflat light-emitting surface 40.

In the transmission grating 110A according to the variational example 1,the first light-transmissive region 10 and the first light-transmissiveplate 111 have the same refractive index, which can substantiallyeliminate reflection at the interface between the firstlight-transmissive region 10 and the first light-transmissive plate 111in the flat light-incident surface 30, and can also increase mechanicalstrength of the transmission grating 110A.

As shown in FIG. 7, the diffraction conditions are the same in thetransmission grating 110A according to the variational example 1 and inthe transmission grating 100 according to the first embodiment.

Variational Example 2

As shown in FIG. 8, the transmission grating 110B according to thevariational example 2 has a configuration similar to that of thetransmission grating 110A of the variational example 1 except that awedge prism 121 made of a transparent material having a refractive indexn₁ is used in place of the first light-transmissive plate 111. Morespecifically, the wedge prism 121 made of a transparent material havinga refractive index n₁ is bonded to the flat light-incident surface ofthe transmission grating 100. The bonding can be carried out in asimilar manner as in the variational example 1, by employing a knownbonding method such as adhesion or welding, using a transparentadhesive. Similarly to that in the variational example 1, thetransmission grating 110B of the variational example 2 as describedabove has increased mechanical strength, and moreover, reflection oflight can be reduced.

That is, in the transmission grating 11B of the variational example 2,by designing the tilting angle of the light-incident surface 121 a ofthe wedge prism 121, the incident angle to the wedge prism 121 can beset to 0° or Brewster's angle θ_(B). FIG. 8 illustrates an example wherethe incident angle to the wedge prism 121 is set to 0°. It is preferablethat the transmission grating 110B of the variational example 2 furtherincludes an antireflection film on the light-incident surface 121 a ofthe wedge prism 121, thus a further reduction in loss due tounintentional reflection can be obtained.

As shown in FIG. 8, in the transmission grating 110B of the variationalexample 2, the optical path difference between two beams of lightincident on the flat light-incident surface 30 at a distance of thediffraction grating period d is d sin α. Because the wavelength in atransparent material of refractive index n₁ is λ/n₁, the conditions forthe first-order diffraction to produce first-order transmitteddiffracted light is expressed in the equation (20).d sin α₁ =λ/n ₁  (20)

Because the equation (2) described in the first embodiment is based onSnell's law, the equation 20 is equivalent to the equation (3).Therefore, λ, n₁, t₁, t₂, and θ satisfy the equation (4-1) or (4-2).

Second Embodiment

The transmission grating 120 according to the second embodiment has asimilar configuration as that of the transmission grating 110A of thevariational example 1 of the first embodiment, except that as shown inFIG. 9B, the second light-reflecting interface 28 a has a curved surfacein the transmission grating 120 according to the second embodiment,while the second light-reflecting interface 28 has a flat surface in thetransmission grating 110A of the variational example 1 of the firstembodiment. The shape of the second light-reflecting interface 28 a doesnot affect the basic diffraction condition, which allows wider choice ofthe shape of the second light-reflecting interface 28 a, such as acurved surface as described above, accordingly wider choice is allowedfor the method to produce the transmission gratings according to certainembodiments of the present disclosure.

The transmission grating 120 according to the second embodiment can beproduced as below, for example. A plurality of plates are provided, ineach of which, as shown in FIG. 9A, the second transparent material 20 ahaving a lower refractive index (n₂) that serves as the secondlight-transmissive region 20 is filled in a pre-determined recess of thefirst transparent plate 10 a having a higher refractive index (n₁) thatserves as the first light-transmissive region 10, and then, the surfaceis polished to obtain a flat surface. Then, the plurality of plates arestacked to form a stacked structure as shown in FIG. 9B, and the stackedstructure is cut by two predetermined parallel planes 80. The materialsdescribed in the first embodiment can also be used for the firsttransparent plates 10 a and the second transparent regions 20 a.

More specifically, the transmission grating 120 according to the secondembodiment can be produced as described below.

With the use of a first transparent material having a high refractiveindex (n₁), a plurality of first transparent plates 10 a each having awidth w₁ and a thickness t₁ and being configured to serve as the firstlight-transmissive region 10 are provided, and at least one groove(width w₂, depth t₂) is formed in a first surface of each of the firsttransparent plates 10 a.

Subsequently, a plurality of second transparent material 20 a having alow refractive index (n₂) is filled in the at least one groove to serveas the second light-transmissive region 20. The surface of the secondtransparent material 20 a filled in the at least one groove may beground or polished if needed so that the surface of the secondtransparent material 20 a and the first surface of the first transparentplate 10 a are coplanar, as shown in FIG. 9A. A plural number of thefirst transparent plates 10 a having the second transparent material 20a as described above are provided.

Subsequently, the plurality of first transparent plates 10 a are stackedsuch that first ends of the second transparent materials 20 a arecoplanar with an intended flat light-incident surface, and the secondends of the second transparent materials 20 a are coplanar with anintended flat light-emitting surface, then, fused to form a stackedstructure of the first transparent plates 10 a.

Then, the stacked structure of the first transparent plates 10 a is cutby two planes 80 that are parallel to and located outer side withrespect to the intended flat light-incident surface 30 and the intendedflat light-emitting surface 40, as shown in FIG. 9B.

According to the transmission grating 120 and the method of producingthe transmission grating 20 as described above, various types oftransmission gratings can be produced by appropriately setting thethickness t₁ of the first transparent plates 10 a, the depth of thegrooves t₂, or the like, with respect to the wavelength λ of thediffracted light, while appropriately setting the high refractive indexn₁ of the first transparent plates 10 a and the low refractive index n₂of the second transparent plates 20 a. In the description above, theupper surface of the second transparent material 20 a filled in thegroove of the first transparent plate 10 a is placed to create the firstlight-reflecting interface 27, but alternatively, the groove may beformed with a flat bottom and the bottom surface of the secondtransparent material 20 a filled in the groove of the first transparentplate 10 a is placed at the first light-reflecting interface side 27.

In the transmission gratings according to the embodiments, the smalleramount of reflection at the time of light incident on the firstlight-transmissive region 10, the more preferable, and thus a method forreducing the reflection has been described, for example in the firstembodiment and the variational examples of the first embodiment. In thefirst embodiment and the variational examples of the first embodiment,it is further preferable to reduce the loss of light due tounintentional reflection at the first lateral surface 21 of the secondlight-transmissive region 20. As described above, when λ, n₁, t₁, t₂,and θ satisfy the relationship 0.5<λ cos θ/n₁(t₁+t₂), the number m ofallowed diffraction orders is limited to 0, 1, and 2. The intensities ofthe reflected and diffracted light of m=0, 1, and 2 are affected by theshape of the first lateral surface 21 of the second light-transmissiveregion 20.

For example, in the configuration shown in FIG. 10A, the first lateralsurfaces 21 of the second light-transmissive regions 20 are in parallelto the flat light-incident surface 30, thus, regular reflection(zero-order reflected and diffracted light 51) of the incident light 50is enhanced.

In the configuration shown in FIG. 10B, the first lateral surfaces 21 ofthe second light-transmissive regions 20 are perpendicular to the fourthlateral surfaces 24 or to the third lateral surfaces 23 of the secondlight-transmissive regions 20, which allows for enhancing thefirst-order reflected and diffracted light 52 that is perpendicular tothe flat light-incident surface 30.

In the configuration shown in FIG. 10C, each of the first lateralsurfaces 21 of the second light-transmissive region 20 is perpendicularto the incident light (that is, line normal to the first lateral surface21 of the second light-transmissive region 20 is in parallel to theincident light), which enhances second-order reflected and diffractedlight 53 that is reflected to the direction of the incident light. Whenthe second-order reflected and diffracted light 53 that is reflected atthe first lateral surface 21 of the second light-transmissive region 20and return to the direction of the incident light has sufficientintensity, an antireflection film may be disposed on the surface at theouter side of the second light-transmissive plate 112 (refractive indexn₁). When the distance between the surface at the outer side of thesecond light-transmissive plate 112 (refractive index n₁) and the flatlight-incident surface 30 is an integer multiple of λ/2n₁, the phases ofthe reflected light from the surface at the outside of the secondlight-transmissive plater 112 (refractive index n₁) and the reflectedlight from the first lateral surface 21 of the second light-transmissiveregion 20 match with each other, further enhancing the second-orderreflected and diffracted light 53.

In order to reduce the intensity of the zero-order and first-orderreflected and diffracted light that will be resulting in optical loss,the first lateral surface 21 of the second light-transmissive region 20shown in FIG. 10C is preferably perpendicular to the incident light.

Third Embodiment

A method of producing a transmission grating according to a thirdembodiment of the present invention will be described below.

The method of producing the transmission grating according to the thirdembodiment includes:

(a) providing two glass plates each having a plurality of elongatedtrapezoidal protrusions formed at an uniform intervals with interveningelongated reverse trapezoidal grooves of reverse trapezoidal shape incross-section;

(b) engaging the elongated trapezoidal protrusions of one of the twoglass plates with the elongated reverse trapezoidal grooves of the otherof the two glass plate to fit the two glass plates to each other; and

(c) closely fitting the walls of one side of the elongated trapezoidalprotrusions with the walls of one side of the elongated reversetrapezoidal grooves, closely fitting the upper surfaces of the elongatedtrapezoidal protrusions with the bottom surfaces of the elongatedreverse trapezoidal grooves, and bonding to each other.

The method of producing the transmission grating of the third embodimentwill be described in detail below.

(a) Providing Glass Plates

Two glass plates 130 each having a first main surface 130 a and a secondmain surface 130 b located opposite to the first main surface areprovided. The two glass plates 130 constitute the firstlight-transmissive regions of the transmission grating, and each glassplate has a high refractive index n₁. The glass plates may be made of anoptical glass material such as a quartz glass, a borosilicate crownglass known as BK7.

Subsequently, as shown in FIG. 11A, a plurality of elongated reversetrapezoidal grooves of reverse trapezoidal shape in a verticalcross-section, each defined by a first lateral surface, a second lateralsurface, and a bottom surface, with an upper opening width a, a bottomwidth b, and a depth h, which hereinafter may be referred to as“elongated reverse trapezoidal groove(s)” or “reverse trapezoidalgroove(s),” are formed in the first main surface 130 a of each of thetwo glass plates provided as above. The plurality of elongated reversetrapezoidal grooves 132 are formed such that, as shown in FIG. 11A, thefirst walls 132 a of the elongated reverse trapezoidal grooves are inparallel to one another and the second walls 132 b of the elongatedreverse trapezoidal grooves are in parallel to one another, where anytwo adjacent elongated reverse trapezoidal grooves are formed at anuniform interval of (a+b−d1). In the present specification, the term “aninterval between two adjacent reverse trapezoidal grooves” refers to adistance between the longitudinal center lines (perpendicular to thevertical cross-section) each extending through the center of the openingof each of the reverse trapezoidal grooves 132. By forming the pluralityof elongated reverse trapezoidal grooves 132 as described above, theelongated trapezoidal protrusions 131 are formed between any two of theadjacent reverse trapezoidal grooves 132. Each of the elongatedtrapezoidal protrusions 131 has an upper surface with a width b−d1, anda bottom surface with a width a−d1, the bottom surfaces of the elongatedtrapezoidal protrusions 131 are coplanar with the bottom surfaces of thereverse-trapezoidal grooves 132. In each of the glass plates 130, thebase portion on which the strip-shaped protrusions 131 are provided isreferred to as a “glass base portion 133”.

The reverse trapezoidal grooves 132 can be formed by, for example, usinga photolithography technique, disposing a metal mask having periodicallyarranged stripes on the first main surface 130 a of the glass plates130, and carrying etching. The etching of the glass plates 130 may becarried out by using a dry-etching device, for example. The shape of thereverse trapezoidal grooves 132, that is, the shape of the trapezoidalprotrusions 131 can be adjusted by the shape of the metal mask and theconditions of etching, such as type of gas(es) and the flow rate(s) fordry etching, the etching pressure, RF power, or the like.

(b) Engaging

As shown in FIG. 11B, using two glass plates 130, the elongatedtrapezoidal protrusions 131 of one of the two glass plates 130 areengaged with the elongated reverse trapezoidal grooves 132 of the otherof the two glass plates 130 to fit the two glass plates 130 to eachother.

(c) Bonding

Subsequently, the first walls 132 a of one of the two glass plates 130are closely fit with the first walls 132 a or the second walls 132 b ofthe other of the two glass plates 130, and the upper surfaces of thetrapezoidal protrusions 131 are closely fit with the bottom surfaces ofthe reverse trapezoidal grooves 132, and are bonded to each other. Thebonding may be carried out by using, for example, a method such aspressure fusing, bonding (it is preferable to use an adhesive that has arefractive index equivalent to the refractive index of the glass plates130), or direct joining, for example, surfaces that are subjected to ahydrophilic treatment are closely fit to join each other.

Accordingly, as shown in FIG. 11C, by joining the glass base portion 133and the elongated trapezoidal protrusions 131 of the two glass plates130 each other, and confining parallel air layers, the transmissiongrating of the variational example 1 having a glass structure of asingle body similar to that of the transmission grating shown in FIG. 7is produced. In the structure shown in FIG. 11C, the firstlight-transmissive regions 10 correspond to that in FIG. 7 are formed byfusing the trapezoidal protrusions 131 of the two glass plates into onebody, and the portions correspond to second light-transmissive regions20 in FIG. 7 are formed with air layers. In the method of producing thetransmission grating according to the third embodiment, it is preferablethat the surface at the incident side of the first light-transmissiveplate 111 and the surface at the light emitting side of the secondlight-transmissive plate 112 are finish polished to form anantireflection film on each surface.

In the transmission grating 110A produced according to the method of thethird embodiment, the second light-transmissive regions 20 are thin airlayers tilted at an tilt angle θ corresponding to the shape of thereverse trapezoidal grooves (or the shape of the trapezoidal protrusions131). The thickness of the air layers (i.e., the secondlight-transmissive regions 20) t₂ is d1 cos θ, and the diffractiongrating period of the transmission grating is a+b−d1. The thickness t₁of the first light-transmissive region 10 is (a+b−2d1)cos θ.

Fourth Embodiment

A method of producing a transmission grating according to a fourthembodiment of the present disclosure will be described below.

The method of producing the transmission grating according to the fourthembodiment includes:

(a) stacking a plurality of thin glass plates of a same thickness with apredetermined space between each two adjacent thin glass plates toobtain a multi-layered glass structure in which each two adjacent thinglass plates are facing each other across the space;

(b) fusing a glass on each side surface of the multi-layered glassstructure to confine the spaces in the multi-layered glass structure;

(c) supporting the multi-layered glass structure containing the confinedspaces by a glass support structure, at an upper surface, a lowersurface, and two lateral surfaces opposite to each other with respect toa central axis that is parallel to the upper surface and the lowersurface of the multi-layered glass structure;

(d) heating the multi-layered glass structure together with the glasssupport structure to collectively soften, and drawing the multi-layeredglass structure and the glass support structure in a direction parallelto the central axis; and

(e) cutting the drawn multi-layered glass structure and the glasssupport structure in a direction parallel to a second plane that isperpendicular to a first plane that includes the central axis and astacking direction of the thin glass plates.

Next, with referring to FIG. 12A to FIG. 16A, the method of producingthe transmission grating according to the fourth embodiment will bedescribed in detail below.

(a) Stacking

A plurality of thin glass plates 141 having a refractive index m and asame thickness are stacked on a base glass plate 140 a via a spacer witha predetermined space each other to obtain a multi-layered glassstructure in which each two adjacent thin glass plates are facing eachother across the space.

More specifically, a plurality of thin glass plates 141 each having athickness T1 and a glass plate 140 a having a greater dimensions thanthat of each of the thin glass plates 141 are provided.

A single thin glass plate 141 is superposed on the upper surface of theglass plate 140 a. At this time, the thin glass plate 141 is superposedsuch that, for example, the central axis of the thin glass plate 141 iscoaxial with the central axis of the upper surface of the glass plate140 a, to expose outer peripheral portion of the upper surface of theglass plate 140 a.

Then, as shown in FIG. 12A, spacer particles 142 such as sphericalsilica particles are scattered with approximately uniform distributionon the upper surface of the thin glass plate 141 that is superposed onthe glass plate 140 a.

Then, as shown in FIG. 12B, another thin glass plate 141 is superposedon the upper surface of the thin glass plate 141 having the spacerparticles 142 scattered thereon.

Scattering the spacer particles 142 on the upper surface of the thinglass plate 141 and superposing another thin glass plate 141 on theupper surface of the thin glass plate 141 having the spacer particles142 scattered thereon are repeated to superpose a necessary number ofthe thin glass plates 141, thus obtaining the multi-layered glassstructure 141L, as shown in FIG. 12C. The space between two adjacentthin glass plates 141 is determined by the diameter of the spacerparticles 142.

(b) Confining

A glass plate 140 b having approximately the same dimensions as theglass plate 140 a is superposed on the upper surface of themulti-layered glass structure 141L, and glass plates 140 c, 140 d, 140e, and 140 f are placed respectively on four lateral surfaces of themulti-layered glass structure 141L, then, the glass plates 140 c, 140 d,140 e, 140 f are fused to the multi-layered glass structure 141L, asshown in FIG. 12D. Accordingly, in the multi-layered glass structure141L, air is confined in the predetermined spaces maintained by thespacing particles 142 between each adjacent two thin glass plates 141,as shown in FIG. 12E, 12F. In the description below, the multi-layeredglass structure 141L sealed by fusing the glass plates 140 a, 140 b, 140c, 140 d, 140 e, and 140 f, and confining air in the confined spacesbetween each adjacent thin glass plates 141 may be referred to as“sealed multi-layered glass structure 141LS”, and the “sealedmulti-layered glass structure 141LS” includes the fused glass plates 140a, 140 b, 140 c, 140 d, 140 e, and 140 f.

(c) Supporting

As shown in FIG. 13, the sealed multi-layered glass structure 141LS issupported by the glass support structure, at the upper surface, thelower surface, and two lateral surfaces opposite to each other withrespect to a central axis (hereinafter may be simply referred to as“central axis c1”) that is in parallel to the upper surface and thelower surface.

More specifically, a circular glass tube 143 having an inner diametergreater than the diagonal length at a cross-section perpendicular to thecentral axis c1 of the sealed multi-layered glass structure 141LS, and alength greater than the length of the sealed multi-layered glassstructure 141LS in the central axis direction is provided, and thesealed multi-layered glass structure 141LS is inserted along the centralaxis direction in the circular glass tube 143. Subsequently, in order tofix the sealed multi-layered glass structure 141LS in the circular glasstube 143, glass rods 144 are inserted in the gap between the inside wallof the circular glass tube and the sealed multi-layered glass structure141LS. FIG. 0.13 shows an example where round rods and polygonal rodsare employed for the glass rods 144. In the description below, astructure that includes the support structure 145 formed with thecircular glass tube 143 and glass rods 144, and the sealed multi-layeredglass structure 141LS supported by the support structure 145 may bereferred to as a preform.

(d) Drawing

The preform including the multi-layered glass structure 141L (sealedmulti-layered glass structure 141LS) and the glass support structure 145are heated and collectively softened, then drawn in the central axis c1direction. The preform includes, for example as shown in FIG. 14, asupport tube 146 provided at each of the both ends of the circular glasstube 143 to support the end of the circular glass tube 143, and anextension tube 147 provided at an end portion of each of the supporttubes. Drawing of the multi-layered glass structure 141L (sealedmulti-layered glass structure 141LS) can be performed with the use of aheating furnace such as those used in manufacturing glass rods whilemeasuring the outer diameter. A schematic diagram of a state afterdrawing is shown in FIG. 15. The ratio of drawing may be determinedbased on the thickness T₁ of each of the thin glass plates 141, distancebetween each adjacent two thin glass plates 141, the thickness of eachof the thin glass plates 141, and distance between each adjacent twothin glass plates 141 that are needed after the drawing.

For example, when the transmission grating is produced by using a thinglass plates 141 of a refractive index n₁, it is preferable to determinethe thickness T₁ of each of the thin glass plates before the drawing,the distance between each adjacent two thin glass plates before thedrawing, and the amount of the drawing, such that the distance t₂between each adjacent two thin glass plates 141 after the drawing, inμm, is in a range of 0.4/4π(n₁ ²−1)^(1/2) to the thickness t₁ of each ofthe thin glass plates after the drawing. The ratio of drawing can be setto, for example, in a range of 100 times to 20,000 times, preferably ina range of 500 times to 10,000 times.

The materials of the circular glass tube 143 and the glass rods 144, andalso of the glass plates 140 a, 140 b, 140 c, 140 d, 140 e, and 140 fcan be selected from the materials that can be integrated with eachother while being drawn. The support structure integrated in the drawingcan serve as a support structure of individual transmission gratingsafter singulating the transmission gratings by cutting as describedbelow.

The glass support structure 145 supporting the sealed multi-layeredglass structure 141LS preferably has a shape of solid revolution (forexample, a combinational shape of a cylindrical shape and a truncatedcone shape). With the support structure in a shape of solid revolution,the whole of the preform can be heated uniformly.

(e) Cutting

As shown in FIG. 16A, together with the drawn glass support structure,the drawn multi-layered glass structure 141L is cut in parallel to asecond plane that is perpendicular to a first plane that includes thecentral axis and a stacking direction of the thin glass plates. Thus, atransmission grating is obtained, in which, as shown in FIG. 16B, thefirst light-transmissive regions 10 and the second light-transmissiveregions 20 of thin air layers are alternately layered. The angle of thesecond plane to the central axis c1 of the second plane can beappropriately set which, for example, corresponds to the tilt angle θ inthe transmission grating 100 of the first embodiment. The distancebetween the two planes 80 cutting the drawn multi-layered glassstructure corresponds to the thickness t of the transmission grating 100of the first embodiment. As described in the first embodiment andothers, in the step of cutting, the angle θ between the second plane andthe central axis c1 and the distance t between the two cut surfaces arepreferably set to satisfy the relationship t₁ cos 2θ/sin θ≤t≤t₁/sin θ.

In the method of producing the transmission grating of the fourthembodiment, the drawn glass support structure is sliced without using aspecific machine such as a very accurate ruling machine (typically usedfor creating grooves of a transmission grating), an exposure machineused in photolithography, or a dry etching machine for etching,accordingly, producing of a large number of the transmission gratingswith high diffraction efficiency can be realized.

Fifth Embodiment

A method of producing a transmission grating according to a fifthembodiment of the present disclosure will be described below.

The method of producing a transmission grating according to a fifthembodiment includes a step of drawing a multi-layered glass structurethat is formed by stacking thin glass plates, which is similar to themethod of producing the transmission grating of the fourth embodiment.However, in the method of producing the transmission grating accordingto the fifth embodiment, spacer particles are not used, and themulti-layered glass structure is formed to contain confined air layers,which is significantly different from the fourth embodiment. Further,cutting is performed quite differently from that in the fourthembodiment.

The method of producing the transmission grating according to the fifthembodiment includes:

(a) providing a plurality of thin glass plates of a same thickness, eachhaving a first main surface, a second main surface opposite to the firstmain surface, a first lateral surface, a second lateral surface, a thirdlateral surface, and a fourth lateral surface; the first main surface ofeach of the thin glass plates defining one or more grooves with apredetermined opening width and extending from the first lateral side tothe third lateral surface opposite to the first lateral surface;

(b) stacking the plurality of thin glass plates so that opening edges oflongitudinal sides defining each of the one or more grooves are alignedinclined at an angle θ with respect to a line normal to the first mainsurface, in a vertical cross-section, to assemble a multi-layered glassstructure;

(c) fusing an end surface portion of the multi-layered glass structurethat includes the first lateral surface of the thin glass plates, an endsurface portion of the multi-layered glass structure that includes thesecond lateral surface of the thin glass plates, an end surface portionof the multi-layered glass structure that includes the third lateralsurface of the thin glass plates, and an end surface portion of themulti-layered glass structure that includes the fourth lateral surfaceof the thin glass plates, to bond adjacent thin glass plates and alsoseal the grooves;

(d) supporting the multi-layered glass structure containing the sealedgrooves with a glass support structure at the upper surface, the lowersurface, the end surface containing the second lateral surfaces of thethin glass plates, and the end surface containing the fourth lateralsurfaces of the thin glass plates and located opposite to the endsurface containing the second lateral surfaces with respect to thecentral axis;

(e) heating the multi-layered glass structure together with the glasssupport structure to collectively soften, and drawing the multi-layeredglass structure and the glass support structure in a direction parallelto the central axis; and

(f) cutting the drawn multi-layered glass structure together with thedrawn glass support structure in a direction parallel to a first planethat is perpendicular to the central axis to obtain a first cut; and

(g) further cutting the obtained first cut that includes a portion ofthe drawn multi-layered glass structure and a corresponding portion ofthe drawn glass support structure in a direction parallel to a secondplane that is in parallel to the extending direction of the grooves toobtain a second cut.

Next, with referring to FIG. 17A to FIG. 19C, the method of producingthe transmission grating according to the fifth embodiment will bedescribed in detail below.

(a) Providing Thin Glass Plates

As shown in FIG. 17A, a plurality of thin glass plates 151 each havingperiodically formed grooves are provided. Each of the thin glass plates151 has a first main surface 151 m 1 and a second main surface 151 m 2opposite to the first main surface 151 m 1, and a first lateral surface151 s 1, a second lateral surface 151 s 2, a third lateral surface 151 s3, and a fourth lateral surface 151 s 4, and a substantially uniformthickness. As shown in FIG. 17A, the first main surface 151 m 1 of eachof the thin glass plates 151 is formed with grooves 152 extending fromthe first lateral surface 151 s 1 side toward the third lateral side 151s 3 side with a predetermined opening width sw, which are arranged fromthe second lateral surface 151 s 2 side toward the fourth lateralsurface 151 s 4 side at a certain period. For the method of forming thegrooves, a known method such as wet etching, dry etching,micro-blasting, superfine finish of surface by grinding, laser beammachining, or a combination of those methods, or the like can be used.Of those, it is preferable to employ a method that can provide a goodflatness in the processed surface, good controllability of groove depth,good controllability of tilt angle of lateral surfaces, and smallreaction force in forming the grooves, example of such methods include alaser-induced backside wet etching method.

(b) Stacking

As shown in FIG. 17B, the plurality of thin glass plates 151 are stackedso that opening edges of longitudinal sides defining each of the grooves(i.e., longitudinal opening edges substantially in parallel to thesecond lateral surface 151 s 2 and the fourth lateral surface 151 s 4)are aligned in a first direction that is inclined at an angle θ withrespect to a line normal to the first main surface, in a verticalcross-section. The angle between the plane including the longitudinalopening edges defining each of the grooves 152 and a line normal to thethin glass plates corresponds to the tilt angle θ of the transmissiongrating of the first embodiment. As shown in FIG. 17C, a single thinglass plate 151 a that is not formed with and groove 152 is superposedon the uppermost surface of the stacked thin glass plates to completethe multi-layered glass structure 151L. The central axis of themulti-layered glass structure 151L is substantially in parallel to thelongitudinal opening edges defining each groove 152.

(c) Sealing

As shown in FIG. 17D and FIG. 17E, an end surface portion of themulti-layered glass structure 151L that includes the first lateralsurface 151 s 1 of the thin glass plates 151, an end surface portion ofthe multi-layered glass structure 151L that includes the second lateralsurface 151 s 2 of the thin glass plates 151, an end surface portion ofthe multi-layered glass structure 151L that includes the third lateralsurface 151 s 3 of the thin glass plates 151, and an end surface portionof the multi-layered glass structure 151L that includes the fourthlateral surface 151 s 4 of the thin glass plates 151, are fused to bondadjacent thin glass plates 151 to seal the grooves 152. Accordingly, thegrooves 152 are sealed.

(d) Supporting

By the glass support structure 145 that is similar to that in the fourthembodiment, the multi-layered glass structure 151L is supported atlocations of the upper surface and the lower surface of themulti-layered glass structure 151L containing the sealed grooves, theend surface 153 including the second lateral surfaces 151 s 2 of thethin glass plates 151, and the end surface 154 containing the fourthlateral surfaces 151 s 4 of the thin glass plates 151 and locatedopposite to the end surface containing the second lateral surfaces withrespect to the central axis.

More specifically, similar to that in the fourth embodiment, themulti-layered glass structure 151L is inserted in the circular glasstube 143, with the central axis of the multi-layered glass structure151L maintained in parallel to the central axis of the circular glasstube 143. Subsequently, in order to fix the sealed multi-layered glassstructure 151L in the circular glass tube 143, glass rods 144 areinserted in the gap between the inside wall of the circular glass tubeand the sealed multi-layered glass structure 151L. As described aboveand shown in FIG. 18, the preform including the support structure 145formed with the circular glass tube 143 and glass rods 144, and thesealed multi-layered glass structure 151L supported by the supportstructure 145 is assembled.

(e) Drawing

In a similar manner as in the fourth embodiment, the multi-layered glassstructure 151L is heated together with the glass support structure 145to be collectively softened, and drawn in a direction in parallel to thecentral axis. In the step of drawing, for example, when the transmissiongrating is produced by using a thin glass plates 151 of a refractiveindex n₁, it is preferable to determine the thickness T₁ of each of thethin glass plates 151 before the drawing, the depth of each of thegrooves before the drawing, and the amount of the drawing, such that thedepth t₂ of each of the grooves defined in each of the thin glass plates151 after the drawing, in μm, is in a range of 0.1/π(n₁ ²−1)^(1/2) tothe thickness t₁ under the grooves of each of the thin glass plates 151after the drawing. As being drawn, the depths of the grooves formed inthe thin glass plates 151 decrease, and also the widths of the groovesformed in the thin glass plates 151 decrease. The ratio of drawing canbe set to, for example, in a range of 100 times to 20,000 times,preferably in a range of 500 times to 10,000 times.

(f) First Cutting

In a first cutting, as shown in FIG. 19A, the drawn multi-layered glassstructure 151L is cut together with the drawn glass support structure145 in a direction parallel to a first plane that is perpendicular tothe central axis to obtain a first cut.

(g) Second Cutting

In a second cutting, as shown in FIG. 19B, the obtained first cut thatincludes a portion of the multi-layered glass structure 151L and acorresponding portion of the glass support structure 145 is further cutin a direction parallel to a second plane 80 that is in parallel to thecentral axis to obtain a second cut. The second plane is substantiallyin parallel to the first direction described in the step of stacking.

The second plane is substantially in parallel to the planes described inthe step of stacking, the planes on which the longitudinal opening edgesdefining the grooves 152 are located. The angle between a line normal tothe first main surface of the thin glass plates and the second planecorresponds to the tilt angle θ in the transmission grating 100 of thefirst embodiment, for example. The product of the groove width after thedrawing and cos θ (i.e., distance between the flat light-incidentsurface and the flat light-emitting surface) corresponds to thethickness t of the transmission grating 100 of the first embodiment. Asdescribed in the first embodiment and other, it is preferable to setsuch that the distance t between the flat light-incident surface and theflat light-emitting surface is in a range satisfying t₁ cos 2θ/sinθ≤t≤t₁/sin θ, that is, the groove width after the drawing is in a rangesatisfying t₁ cos 2θ/sin θ cos θ≤t≤t₁/sin θ cos θ.

According to the method of producing the transmission grating accordingto the fifth embodiment, the transmission grating that is free from thescattering of light caused by the spacer particle, and exhibits highdiffraction efficiency can be produced. Moreover, the thickness t (i.e.,distance between the flat light-incident surface and the flatlight-emitting surface) can be controlled mainly by the width of thegrooves in the step of providing the thin glass plates, and the amountof drawing in the step of drawing. Thus, obtaining desired dimensions iseasier than by employing polishing whose dimensional accuracy is±several microns. According to the method of producing the transmissiongrating according to the fifth embodiment, producing of a large numberof the transmission grating with high diffraction efficiency can berealized with good production yield.

EXAMPLES Example 1

In Example 1, the transmission grating in which the firstlight-transmissive region 10 is made of a transparent quartz glass andthe second light-transmissive region 20 is the air, will be producedaccording to the method of producing the transmission grating of thethird embodiment.

Steps of producing in the Example 1 will be described below in dueorder.

Providing Glass Plate

Two transparent quartz glass plates (refractive index 1.46) areprovided.

Processing Glass Plate

On each of the transparent quartz glass plates provided as describedabove, a Cr metal film is disposed by using a sputtering method, andthen a resist film is disposed thereon by using a spin coating method.Subsequently, using a photolithography technique (stepper, electron beamdrawing device, etc.), the resist film is exposed to predetermined lightat a predetermined period with a pitch of 3.16 μm, then, the resist isdeveloped to obtain a resist pattern of periodically aligned stripeshapes, on the metal film. Subsequently, using the elongated resistpattern as a mask, the Cr metal film under the mask is dry-etched byusing a dry-etching machine (for example, an inductively-coupled plasmareactive ion etching (ICP-RIE) machine), and further, using the Cr metalfilm as a mask and using the dry-etching machine, the transparent quartzglass plate is etched. The shape to be obtained by etching can becontrolled by the shape of the metal mask and the dry-etching conditions(such as type of gas(es) and the flow rate(s) for dry etching, theetching pressure, RF power, or the like). In the production of thetransmission grating of Example 1, dry-etching is carried out whileadjusting the dry-etching conditions as needed, to obtain the resultingshapes matched to a designed shape. The Cr metal film mask remains onthe quartz glass plate is removed by using an etchant that intended toexclusively dissolve Cr. Thus, two glass plates 130 each made oftransparent quartz glass formed with the elongated trapezoidalprotrusions 131 between elongated reverse trapezoidal grooves 132, asshown in FIG. 11A are provided. In the glass plates 130, the pitch ofthe trapezoidal protrusions 131 (i.e., diffraction grating period) is3.16 μm, the width of upper surfaces of the protrusions is 1.52 μm, thewidth at the bottom of the trapezoidal protrusions is 1.60 μm, and theheight of the protrusions is 0.76 μm.

Engaging

Subsequently, as shown in FIG. 11B, one of the two glass plates 130 isturned over and superposed on the second glass plate 130 such that therecesses and the protrusions of the two glass plates 130 are engagedwith each other, and one of the glass plates 130 is pushed to one sideso that the two glass plate 130 are in contact with each other at oneside of lateral wall surfaces.

Bonding

Subsequently, as shown in FIG. 11C, while maintaining one of the twoglass plates being pushed to one side as described above, the two glassplates 130 are integrally bonded. As described above, the transmissiongrating of quartz glass formed with integrally bonded two protrudingportions 131 and two glass base portions 133, confining thin air layersaligned at a tilt angle θ is obtained. The bonding may be carried out byusing a method such as pressure fusing or bonding (using an adhesivethat has a refractive index equivalent to the refractive index of thequartz glass, or direct joining.

At last, finish polishing is applied on the surfaces at the incidentside and the light-emitting side. The transmission grating produced asdescribed above has the values of; θ≈3.01°, t₁≈3117 nm, and t₂≈39 nm.The surface at the incident side is provided with an antireflectionlayer made of a dielectric multilayer film and the surface at theemission side is provided with a reflection control layer made of adielectric multilayer film. As illustrated in FIG. 11D, when light of awavelength λ=488 nm is incident on the flat light-incident surface at anangle of 8.9° with respect to the line normal to the flat light-incidentsurface, the wavelength of the light in the quartz glass becomes 334 nmand at an angle of 6.08°, passes through the transmission grating inwhich thin layers of air are aligned at an angle 3° with respect to theline normal to the flat light-incident surface, then first-ordertransmitted diffracted light 61 is emitted from the flat light-emittingsurface in a direction perpendicular to the flat light-emitting surface.

The transmission grating of Example 1 produced as described above doesnot have a metal or the like that absorbs light on the optical path,which can eliminate generation of heat due to absorption of light and/ordeterioration due to the generated heat. Thus, even when operated withhigh optical density, deviation of optical path caused by the generatedheat and deterioration of the component due to light can be negligible,and reliability of the transmission grating can be improved.

The glass plate 130 having periodically provided elongated trapezoidalprotrusions can singly serve as a transmission grating, but thetransmission grating of Example 1 has a configuration in which the first(or second) lateral surfaces defining the elongated reverse trapezoidalgrooves of one of the two glass plates 130 are closely fit with thefirst (or second) lateral surfaces of the elongated trapezoidalprotrusions of the other one of the two glass plates 130, and bonded toeach other. With this configuration, intensity of second-ordertransmitted diffracted light is reduced compared to that of a singletransmission grating, and intensity of the first-order transmitteddiffracted light can be enhanced. Because two glass plates (i.e.,transmission gratings) are integrated together, higher mechanicalstrength than that of a single glass plate (i.e., transmission grating).Alternatively, a first and a second two transmission gratings of thesame diffraction grating period that can be engaged to each other withthe protrusions of the first transmission grating and the recesses ofthe second transmission grating, the lateral surfaces of the protrusionsof the first transmission grating and the lateral surfaces of therecesses of the second transmission grating being substantially inparallel to each other can also be used.

Example 2

In Example 2, a transmission grating that can further reduce zero-ordertransmitted diffracted light 60 compared to that in Example 1 isproduced according to the method illustrated in the fourth embodiment.Steps of producing in Example 2 will be described below.

Providing Thin Glass Plates

A plurality of thin glass plates 141 having the same width, length, andthickness (for example, refractive index 1.51, thickness 0.05 mm, width500 mm, and length 1,000 mm) are provided.

Stacking

A single glass plate 140 a with a thickness of 7 mm (width 514 mm,length 1,014 mm) is provided, and one of the thin glass plates 141 isplaced co-center on the glass plate 140 a with its peripheral edgessubstantially in parallel to the peripheral edges of the glass plate 140a. As shown in FIG. 12A, spacer particles 142 (for example, sphericalsilica particles of diameter 5 μm used in manufacturing liquid crystals)are spread in dry conditions on the thin glass plate 141 insingle-particle state. Then, as shown in FIG. 12B, another one of thethin glass plates 141 is superposed on the thin glass plate 141 that hasbeen placed on the glass plate 140 a. Scattering the spacer particles142 and superposing the thin glass plates 141 are alternately repeatedto form the multi-layered glass structure 141L having 10,000 superposedthin glass plates 141, shown in FIG. 12C. The superposing is performedin air, so that the spacer particles 142 and air are interposed betweenadjacent thin glass plates 141.

Sealing

Further, the lateral surfaces and the upper surface of the multi-layeredglass structure 141L are respectively covered by a glass plate of 7 mmthickness 140 b to 140 f. The glass plates 140 a to 140 f are thermallyfused to the upper and lower surfaces and the lateral surfaces of themulti-layered glass structure 141L, to obtain the sealed multi-layeredglass structure 141LS shown in FIG. 12D. At this time, the outerperipheral portions of each of the thin glass plates 141 are thermallyfused to corresponding portions of the glass plates of 7 mm thickness140 c to 140 f that surround the lateral surfaces of the multi-layeredglass structure 141L. Accordingly, layers of air are confined betweenthe thin glass plates 141.

Supporting

Further, the sealed multi-layered glass structure 141LS is inserted inthe circular glass tube (thickness of 7 mm, inner diameter of 765 mm)143 and the glass rods 144 are inserted to fill the gap between theinside wall of the circular glass tube and the sealed multi-layeredglass structure 151L. As shown in FIG. 13 and FIG. 14, the glass supportincludes the circular glass tube 143 and the glass rods 144. Asdescribed above, the preform is formed with the sealed multi-layeredglass structure LS and the glass support structure. Forming the glasssupport structure in a shape of solid revolution (for example, acombinational shape of a cylindrical shape and a truncated cone shape)is to achieve uniform heating in the step of drawing.

Drawing

Next, heat is applied and the preform is drawn in the direction of itscentral axis. By drawing the preform about 916 times gives the sealedmulti-layered glass structure LS (glass assembly rod) with an outerdiameter of 25.7 mm, shown in FIG. 15. With the air in the multi-layeredglass structure L kept confined, the air between the glass supportstructure and the multi-layered glass structure L is discharged whiledrawing, through the support tube 146 and the extension tubes 147, fromthe openings of the preform. At this time, the circular glass tube 143and the glass rods 144 are thermally fused to integrate together.Meanwhile, the portions of the multi-layered glass structure L confiningthe layers of air are drawn and become thin gaps containing air. Afterbeing drawn, the arrangement period of the thin glass plates is about1/30.3 of that in the preform, which gives a period of 1.817 μm (1.652μm thickness of each thin glass plate, 0.165 μm thickness of each airlayer).

Cutting

As shown in FIG. 16A, the multi-layered glass structure L (a shape ofsolid revolution) is sliced with a thickness of 1 mm, along a planeperpendicular to a plane including the central axis that issubstantially parallel to the drawing direction of the multi-layeredglass structure L (a shape of solid revolution) and also substantiallyparallel to a plane tilted at an angle θ of 9.97° to a line normal tothe thin glass plates 141, to obtain a plurality of slices of glassassembly (FIG. 16B). One planar side of the slices of glass assembly(FIG. 16B) are optically polished, and the polished surface is bonded toa double-side optically polished thick glass plate (thickness of 5 mm,refractive index of 1.51). At this time, bonding is carried out so thatair bubbles or the like do not enter the interface of bonding. Thebonding can be carried out by employing a known bonding method, forexample, using a transparent adhesive or thermally fusing. In order toprevent polishing particles from entering the slices of glass assembly(i.e., between the thin glass plates) at the time of polishing,polyvinyl alcohol (PVA) or the like may be filled between the thin glassplates in the slices of glass assembly, which can be removed after thepolishing, by using warm water or an organic solvent.

Optical Polishing

Each of the other planar surfaces of the slices of glass assembly ispolished to reduce the thickness and optical polishing is applied suchthat the diffraction grating (a layered structure of thin glass platesand air layers in a slice of glass assembly) has a thickness t of 9 μm(a thickness in arrange of 8.97 μm to 9.54 μm), that is, a totalthickness of the diffraction grating and the thick glass plate(thickness of 5 mm) 5.009 mm.

Bonding Thick Glass Plate

A thick glass plate (thickness of 5 mm, refractive index of 1.51) isbonded on the polished surface of each of the diffraction gratings.Thus, a plurality of transmission gratings (one of which is shown inFIG. 7) are produced.

Disposing Dielectric Multilayer Film

In the transmission grating of Example 2, an antireflection film made ofa dielectric multilayer film (for example, Al₂O₃ film (refractive index1.64)/ZrO₂ film (refractive index 2.00)/MgF₂ film (refractive index1.38)) is further disposed on the polished surface of one of the thickglass plates to serve as the flat light-incident surface of the laserlight. A dielectric multilayer film of a desired reflectance is disposedon the polished surface of the other one of the thick glass plates toadjust the amount of second-order reflected and diffracted light feedingback to the laser.

In the transmission grating of Example 2, as described above, the glassassembly (glass assembly rod) is sliced in parallel to a plane thattilts at angle (θ=9.97°) to the line normal to the thin glass plates141, thus, the diffraction grating period is 1.845 μm.

When the p-polarized constituent of a linearly polarized laser light ofwavelength 950 nm is incident on the flat light-incident surface of thetransmission grating of Example 2 at an incident angle 31°, according toSnell's law, the laser light is refracted at an angle of refraction of19.94° at the interface between air and the thick glass plate ofrefractive index 1.51. With the wavelength 629 nm in the thick glassplate, the laser light propagates toward the diffraction grating regionwith a diffraction grating period of 1.845 μm. The conditions for thefirst-order diffraction are satisfied, enhancing the intensity of thefirst-order diffracted light, and first-order transmitted diffractedlight is emitted in a direction normal to the thick glass plate. Withthe incident angle 31°, the allowed diffraction orders are limited to 0,1, and 2, with the diffraction angles 31°, 0°, and −31°, respectively.Light propagating in each of the thin glass plates is incident on theinterface between the thin glass plate and air at an incident angle of80.03° that is greater than the critical angle of 41.47°, thussatisfying the condition for total internal reflection. The thickness ofeach of the air layers is 0.1652 μm, which is 17.4% of the wavelength950 nm, and greater than twice the thickness of the evanescent field(i.e., a thickness 7.2% of the wavelength at an incident angle 80.03°.Thus, the intensity of transmitted light is negligible. The diffractiongrating has a thickness of 9 μm, allowing substantial elimination ofzero-order transmitted diffracted light that rectilinearly propagatingin the thin glass plate without incident on the interface between thethin glass plate and air layer. Generally, except for the intensity ofzero-order diffracted light, the intensity of first-order diffractedlight is greater than the intensity of second- or higher-orderdiffracted light, accordingly, incident light can be efficientlyconverted to the first-order diffracted light.

After slicing the glass assembly to about 1 mm thickness, the thicknessof the sliced glass assembly is further reduced to about 9 μm toeliminate or reduce multiple reflections in the thin glass plateslocated between thin air layers. The thickness about 9 μm does not havesufficient mechanical strength for handling, thus a thick glass plate isbonded on both planar sides. In conventional transmission gratings,reflected light at the upper surface and the lower surface ofdiffraction grating will be resulting in optical loss. However, in thetransmission grating of Example 2 the diffraction grating is placedbetween the thick glass plates of a same refractive index, which caneliminate or reduce specularly reflected light but allows specularreflected light (and first-order and second-order reflected anddiffracted light) at the incident-side edge of the thin layer of 0.165μm thickness. The surface of thick glass plate to serve as the laserlight incident surface is provided with the antireflection film made ofa dielectric multilayer film, which allows reducing the occurrence ofreflected light.

In the method of producing according to Example 2, the transmissiongratings are obtained by slicing the multi-layered glass structure LS(glass assembly rod), which allows producing a number of transmissiongratings at once, and thus has good mass productivity compared to themethods in which individual diffraction gratings are engraved by usingelectron beam drawing technique or interference exposure technique.According to the Example 2, the preform of 1,000 mm length is drawn toabout 916 times and sliced to 1 mm thickness, thus, 900,000 or morediffraction gratings can be produced.

The transmission grating of Example 2 produced as described above doesnot have a metal or the like that absorbs light on the optical path,which can substantially eliminate generation of heat and/ordeterioration due to absorption of light. Thus, even when operated withhigh optical density, deviation of optical path caused by the generatedheat and deterioration of the component due to light can be negligible,and reliability of the transmission grating can be improved.

In place of spreading the spacer particles 142 (spherical silicaparticles) in single-particle state, a plurality of protrusions may beformed on the surfaces of the thin glass plates by etching or the like.When the thin glass plates have a first surface and a second surfaceopposite to the first surface and the first surface is smoother than thesecond surface, the first surface is used to form the light-firstreflecting interface 27. A plurality of protrusions may be formed byetching or the like on the second surfaces of the thin glass plates, andthe etched surfaces are placed as the lower surfaces of the firstlight-transmissive regions 10. This is to enhance first-ordertransmitted diffracted light by reflect light at the light-firstreflecting interface 27. Stacking of the thin glass plates may beperformed by winding a thin glass sheet onto a spinning square pillar,and cutting the wound thin glass sheet at each edge of the squarepillar.

Example 3

In Example 3, a transmission grating is produced according to the methodillustrated in the fifth embodiment. Steps of producing in Example 3will be described below.

Providing Thin Glass Plate with Grooves

A plurality of thin glass plates 151 of a same thickness (for example,refractive index 1.51, thickness 0.03 mm, width 500 mm, and length 500mm) each formed with a plurality of grooves 151 in one surface (a firstmain surface) are provided.

In Example 3, for example, six grooves 152 are formed in the drawingdirection in the first main surface of each of the thin glass plates,with a length of 450 mm, a depth of 1.5 μm, a bottom width of 160 μm,and a period of 92 mm. As shown in FIG. 17A, the six grooves are formedsuch that a flat portion with a width of about 20 mm is left between theouter peripheral edge of the thin glass plates 151 and the edges of thegrooves. For the method of forming the grooves, a known method such aswet etching, dry etching, micro-blasting, superfine finish of surface bygrinding, laser beam machining, or a combination of those methods, orthe like can be used. It is preferable to employ a method that canprovide a good flatness in the processed surface, good controllabilityof groove depth, good controllability of tilt angle of lateral surfacesdefining the grooves, and small reaction force in forming the grooves,example of such methods include a laser-induced backside wet etchingmethod illustrated in Japanese Unexamined Patent Application PublicationNo. 2004-306134.

In Example 3, when the angle between the longitudinal lateral surfacesdefining the grooves with an isosceles trapezoid shape in a crosssection and the line normal to the thin glass plate is 9.82°, theintensity of second-order reflected and diffracted light incident on anedge of air layer at an angle of 19.64° can be increased and theintensity of zero-order and first-order reflected and diffracted lightcan be reduced. With this configuration, at the time of feeding back thesecond-order reflected and diffracted light to the external resonatorlaser, sufficient feedback amount can be reliably obtained.

Further, in Example 3, in order to reflect light at the bottom surfacesof the grooves and in order to reduce scattering loss of light, thebottom surfaces of the grooves are preferably made smooth. Thisconfiguration can increase the intensity of first-order transmitteddiffracted light to be used, and can reduce second-order transmitteddiffracted light that will be resulting in optical loss, and thereforepreferable.

Stacking

As shown in 17B, 10,000 of the thin glass plates 151 formed with thegrooves 152 as described above are stacked. Stacking is performed suchthat the first main surface of thin glass plate 151 formed with thegrooves is in contact with the second main surface of the thin glassplate 151 formed with the grooves that is placed on the first mainsurface. Further, in the stacking, the long-side directions of thegrooves 152 of the thin glass plates 151 are aligned in parallel to thedrawing direction, with the long-side edges of the grooves 152 ofcorresponding thin glass plates 151 laid on the same plane. The planeincluding the long-side edges described above is tilted at 9.82° to theline normal to the first main surfaces of the thin glass plates 151. Asshown in FIG. 17C, a single thin glass plate 151 a that is not formedwith and groove 152 is superposed on the uppermost surface of thestacked thin glass plates to complete the multi-layered glass structure151L.

Sealing

At the surface and near-surface portion of the four lateral surfaces ofthe multi-layered glass structure 151L, the thin glass plates 151 arethermally fused to each other to confine the air in the grooves 152, asshown in FIG. 17D and FIG. 17E.

Drawing

Further, the multi-layered glass structure 151L is inserted in thecircular glass tube 143 (thickness of 7 mm, inner diameter of 771 mm)and glass rods 144 are inserted to fill the gap between the inside wallof the circular glass tube and the sealed multi-layered glass structure151L, and the both ends of the circular glass tube are narrowed toobtain a preform. Subsequently, the preform is placed in a drawingmachine and heat is applied, and then heated preform is drawn. InExample 3, the preform is drawn to about 916 times to obtain the outerdiameter of 23.44 mm. In this state, the period of the grooves thatconfine thin layers of air become about 1/33.5 of that in the preform,which gives a period in the stacking direction of 0.896 μm (in which, athickness t1 from the bottom of a groove to the upper surface ofadjacent groove is ≈0.8512 μm, thickness t₂ of air layer confined ineach groove is ≈0.0448 μm, and the bottom width of each groove is 4.776μm), and a period in the direction perpendicular to the stackingdirection of ≈2.75 mm.

Cutting

As shown in FIG. 19A, the extended multi-layered glass structure 151L(glass assembly rod in a cylindrical shape) is cut, for example, inparallel to a plane perpendicular to the central axis of themulti-layered glass structure 151L, to a length of 30.3 mm. Then, thecut portion of the extended multi-layered glass structure 151L isfurther sliced in parallel to a plane in parallel to the central axisand tilt at 9.82° to a line normal to the first surfaces of the thinglass plates, to a thickness of 2.5 mm (with a cutting margin of 0.25mm), by using, for example, a wire saw, to obtain six rectangular glassplates (width of about 23 mm, a length of 30.3 mm, and a thickness of2.5 mm). According to Example 3, 100,000 or greater diffraction gratingscan be produced from a single preform of a length of 500 mm (FIG. 19B).The slicing is performed such that the array of air layers of thegrooves is located approximately the center of the thickness of eachsliced plated. In this case, the array of air layers of the grooves thatconstitute the diffraction grating is located at the center region ofeach of the rectangular glass plates, with an aspect ratio of 2:1.

Optical Polishing

The both sides of the glass plates obtained by slicing the portions ofthe glass assembly rod as described above are optically polished. Whenthe glass plate is placed so that the cross-section of the grooves is ina reverse trapezoidal shape, the upper surface of the glass plate servesas the light incident surface and the lower surface of the glass plateserves as the light emission surface. By adjusting the thickness ofslicing, the amount of polishing can be adjusted, and the step ofbonding a thick glass plate as in Example 2 can be omitted.

Disposing Dielectric Multilayer Film

In Example 3, an antireflection film made of three layers of dielectricfilm is disposed on the light-emitting side of the transmission grating.At this time, the surface at the light-emitting side can be made to apartially reflecting mirror, which allows adjustment of the amount offeedback the semiconductor laser by the reflectance of the dielectricmultilayer film. With this configuration, the need of an externalpartially reflecting mirror in a WBC laser device can be eliminated. Byintegrally structuring the partially reflecting mirror that has beenprovided externally with the diffraction grating, locationalmisalignment that has been occurred between the external partiallyreflecting mirror and the diffraction grating can be eliminated andreliability of the laser device can be improved.

When the transmission grating produced in Example 3 is used in a WBClaser device, the rectangular glass plate is arranged such that thearray of air layers of the grooves that constitutes the diffractiongrating is placed perpendicular to the horizontal plane of incidence(which includes the optical axis), to allow, for example, ellipticalp-polarized semiconductor laser light (wavelength of 460 nm, and anellipticity ratio (the ratio of major axis (12 mm) and minor axis (6 mm)is 2:1) to be incident on the plane of incidence at an angle of 30.5°.According to Snell's law, the incident light is refracted at theinterface (corresponding to the surface outer side of the firstlight-transmissive plate 111 in FIG. 7) between air and the glass at anangle of refraction 19.64°. The thicknesses of the air layers of thegrooves are smaller than the glass, thus most of incident light islinearly propagates in the glass and incident on the interface (i.e.,light-first reflecting interface 27) between the glass at the bottom ofthe groove and air layer at an incident angle of 80.18°. The incidentangle is greater than the critical angle of 41.47°, thus the incidentlight is totally internally reflected at the light-first reflectinginterface 27. This is because the thickness 0.0448 μm of the air layersof the grooves corresponds to 9.7% of the wavelength 460 nm and greaterthan the thickness 7.22% of the evanescent field. Thus, the intensity oftransmitted light is negligible. Meanwhile, the width of about 4.8 μm ofthe air layers of the grooves is not small enough to allow linearlypropagating light transmitting through without being reflected, but alsolarge enough to allow reflected light to be reflected at the interface(second light-reflecting interface) at the upper surface of adjacentgroove. Thus, zero-order diffracted light can be sufficiently reduced.The first-order transmitted diffracted light specularly reflected onceat the light-reflecting interface propagates perpendicularly to thelight-reflecting interface (i.e., a surface corresponding to outer-sidesurface of the second light-transmissive plate 112 in FIG. 7). Thepropagating direction of the incident light in the glass and theinterface between glass and air at the flat light-incident surface sideof the air layer are perpendicular to each other. Thus, incident lightat the edge of the thin air layer is reflected and returns to thesemiconductor laser as second-order reflected and diffracted light.Also, the light reflected at the light-emitting side of the interfacemade into a partially reflecting mirror is retroreflectively reflectedto the semiconductor laser as second-order reflected and diffractedlight.

In the step of forming the grooves in Example 3, shallow grooves of adepth of 1.5 μm are formed, but in the case where a laser-inducedbackside wet etching method is employed, deep grooves of an aspect ratiogreater than 100 can be formed. Thus, transparent glass plates (athickness of 2 mm) formed with deep grooves can be used in place of theglass plates formed with the shallow grooves.

The transmission gratings described in the embodiments and examplesabove can be used as a wavelength dispersive element in wavelength beamcombining light emitting devices. Accordingly, the transmission gratingsdescribed in the embodiments and examples above can be used in lightemitting devices in various industrial applications (such as heating,cutting, welding). Also, the transmission gratings described in theembodiments and examples above can be used as a wavelength dispersiveelement in optical apparatus such as spectroscopes.

Obviously, numerous modifications and variations of the presentinvention are possible in light of the above teachings. It is thereforeto be understood that within the scope of the appended claims, theinvention may be practiced otherwise than as specifically describedherein.

What is claimed is:
 1. A laser device comprising: a laser arrayconfigured to emit a plurality of laser beams of different wavelengthsλ_(i) to one another from different positions; a transmission gratingcomprising: a plurality of first light-transmissive regions having arefractive index of n₁, and a plurality of second light-transmissiveregions having a refractive index of n₂ that is smaller than n₁, whereinthe first light-transmissive regions and the second light-transmissiveregions are alternately disposed, wherein the transmission grating has aflat light-incident surface and a flat light-emitting surface, and adiffraction grating period of d, wherein, among a plurality ofinterfaces between the first light-transmissive regions and the secondlight-transmissive regions, light-reflecting interfaces on which lighttransmitted through the first light-transmissive regions is incident arein parallel with one another and are inclined such that a line normal toeach of the light-reflecting interfaces is at an inclination angle θwith respect to the flat light-incident surface and to the flatlight-emitting surface, wherein 0°<θ<90°, and wherein, when a thicknessof the first light-transmissive regions in a direction perpendicular tothe light-reflecting surfaces is t₁ and a thickness of the secondlight-transmissive regions in a direction perpendicular to thelight-reflecting surfaces is t₂, the thickness t₂, in μm, is in a rangeof 0.1/π(n₁ ²−n₂ ²)^(1/2) to t₁; and an optical system located betweenthe laser array and the transmission grating, and configured to directthe plurality of laser beams of different wavelengths λ_(i) emitted fromthe laser array to be incident on the flat light-incident surface of thetransmission grating at an incident angle α_(i) corresponding to each ofthe plurality of laser beams of different wavelengths λ_(i); whereineach of the wavelengths λ_(i) and the incident angle α_(i) correspondingto the wavelength Δ_(i) satisfies d sin α_(i)=λ_(i).
 2. The laser deviceaccording to claim 1, wherein a distance t between the flatlight-incident surface and the flat light-emitting surface is in a rangeof t₁ cos 2θ/sin θ to t₁/sin θ.
 3. A transmission grating comprising: aplurality of first light-transmissive regions having a refractive indexof n₁; and a plurality of second light-transmissive regions having arefractive index of n₂ that is smaller than n₁; wherein the firstlight-transmissive regions and the second light-transmissive regions arealternately disposed; wherein the transmission grating has a flatlight-incident surface and a flat light-emitting surface, and adiffraction grating period of d; wherein, among a plurality ofinterfaces between the first light-transmissive regions and the secondlight-transmissive regions, light-reflecting interfaces on which lighttransmitted through the first light-transmissive regions is incident arein parallel with one another and are inclined such that a line normal toeach of the light-reflecting interfaces is at an inclination angle θwith respect to the flat light-incident surface and to the flatlight-emitting surface, wherein 0°<θ<90°; wherein, when a thickness ofthe first light-transmissive regions in a direction perpendicular to thelight-reflecting surfaces is t₁ and a thickness of the secondlight-transmissive regions in a direction perpendicular to thelight-reflecting surfaces is t₂, the thickness t₂, in is in a range of0.1/π(n₁ ²−n₂ ²)^(1/2) to t₁; wherein the transmission grating isconfigured such that, when a plurality of laser beams of differentwavelengths λ_(i) to one another are incident on the flat light-incidentsurface of the transmission grating at an incident angle α_(i)corresponding to each of the plurality of laser beams of differentwavelengths λ_(i), diffracted light ray groups are emittedperpendicularly from the flat light-emitting surface of the transmissiongrating; wherein each of the wavelengths λ_(i) and the incident angleα_(i) corresponding to the wavelength λ_(i) satisfies dsinα_(i)=λ_(i).4. The transmission grating according to claim 3, wherein a distance tbetween the flat light-incident surface and the flat light-emittingsurface is in a range of t₁ cos 2θ/sin θ to t₁/sin θ.
 5. Thetransmission grating according to claim 3, further comprising adielectric multilayer film on the flat light-emitting surface.
 6. Thetransmission grating according to claim 4, further comprising adielectric multilayer film on the flat light-emitting surface.